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On the number of solutions of some transcendental equations | We give upper and lower bounds for the number of solutions of the equation
$p(z)\log|z|+q(z)=0$ with polynomials $p$ and $q$.
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Relaxation of p-growth integral functionals under space-dependent differential constraints | A representation formula for the relaxation of integral energies
$$(u,v)\mapsto\int_{\Omega} f(x,u(x),v(x))\,dx,$$ is obtained, where $f$
satisfies $p$-growth assumptions, $1<p<+\infty$, and the fields $v$ are
subjected to space-dependent first order linear differential constraints in the
framework of $\mathscr{A}$-quasiconvexity with variable coefficients.
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Simultaneous shot inversion for nonuniform geometries using fast data interpolation | Stochastic optimization is key to efficient inversion in PDE-constrained
optimization. Using 'simultaneous shots', or random superposition of source
terms, works very well in simple acquisition geometries where all sources see
all receivers, but this rarely occurs in practice. We develop an approach that
interpolates data to an ideal acquisition geometry while solving the inverse
problem using simultaneous shots. The approach is formulated as a joint inverse
problem, combining ideas from low-rank interpolation with full-waveform
inversion. Results using synthetic experiments illustrate the flexibility and
efficiency of the approach.
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Critical neural networks with short and long term plasticity | In recent years self organised critical neuronal models have provided
insights regarding the origin of the experimentally observed avalanching
behaviour of neuronal systems. It has been shown that dynamical synapses, as a
form of short-term plasticity, can cause critical neuronal dynamics. Whereas
long-term plasticity, such as hebbian or activity dependent plasticity, have a
crucial role in shaping the network structure and endowing neural systems with
learning abilities. In this work we provide a model which combines both
plasticity mechanisms, acting on two different time-scales. The measured
avalanche statistics are compatible with experimental results for both the
avalanche size and duration distribution with biologically observed percentages
of inhibitory neurons. The time-series of neuronal activity exhibits temporal
bursts leading to 1/f decay in the power spectrum. The presence of long-term
plasticity gives the system the ability to learn binary rules such as XOR,
providing the foundation of future research on more complicated tasks such as
pattern recognition.
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Harnessing functional segregation across brain rhythms as a means to detect EEG oscillatory multiplexing during music listening | Music, being a multifaceted stimulus evolving at multiple timescales,
modulates brain function in a manifold way that encompasses not only the
distinct stages of auditory perception but also higher cognitive processes like
memory and appraisal. Network theory is apparently a promising approach to
describe the functional reorganization of brain oscillatory dynamics during
music listening. However, the music induced changes have so far been examined
within the functional boundaries of isolated brain rhythms. Using naturalistic
music, we detected the functional segregation patterns associated with
different cortical rhythms, as these were reflected in the surface EEG
measurements. The emerged structure was compared across frequency bands to
quantify the interplay among rhythms. It was also contrasted against the
structure from the rest and noise listening conditions to reveal the specific
components stemming from music listening. Our methodology includes an efficient
graph-partitioning algorithm, which is further utilized for mining prototypical
modular patterns, and a novel algorithmic procedure for identifying switching
nodes that consistently change module during music listening. Our results
suggest the multiplex character of the music-induced functional reorganization
and particularly indicate the dependence between the networks reconstructed
from the {\delta} and {\beta}H rhythms. This dependence is further justified
within the framework of nested neural oscillations and fits perfectly within
the context of recently introduced cortical entrainment to music. Considering
its computational efficiency, and in conjunction with the flexibility of in
situ electroencephalography, it may lead to novel assistive tools for real-life
applications.
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Some characterizations of the preimage of $A_{\infty}$ for the Hardy-Littlewood maximal operator and consequences | The purpose of this paper is to give some characterizations of the weight
functions $w$ such that $Mw$ is in $A_{\infty}$. We show that for those weights
to be in $A_{\infty}$ ensures to be in $A_{1}$. We give a criterion in terms of
the local maximal functions $m_{\lambda}$ and we present a pair of
applications, among them someone similar to the Coifman-Rochberg
characterization of $A_{1}$ but using functions of the form $(f^{\#})^{\delta}$
and $(m_{\lambda}u)^{\delta}$ instead of $(Mf)^{\delta}$.
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Magma oceans and enhanced volcanism on TRAPPIST-1 planets due to induction heating | Low-mass M stars are plentiful in the Universe and often host small, rocky
planets detectable with the current instrumentation. Recently, seven small
planets have been discovered orbiting the ultracool dwarf
TRAPPIST-1\cite{Gillon16,Gillon17}. We examine the role of electromagnetic
induction heating of these planets, caused by the star's rotation and the
planet's orbital motion. If the stellar rotation and magnetic dipole axes are
inclined with respect to each other, induction heating can melt the upper
mantle and enormously increase volcanic activity, sometimes producing a magma
ocean below the planetary surface. We show that induction heating leads the
three innermost planets, one of which is in the habitable zone, to either
evolve towards a molten mantle planet, or to experience increased outgassing
and volcanic activity, while the four outermost planets remain mostly
unaffected.
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Coqatoo: Generating Natural Language Versions of Coq Proofs | Due to their numerous advantages, formal proofs and proof assistants, such as
Coq, are becoming increasingly popular. However, one disadvantage of using
proof assistants is that the resulting proofs can sometimes be hard to read and
understand, particularly for less-experienced users. To address this issue, we
have implemented a tool capable of generating natural language versions of Coq
proofs called Coqatoo, which we present in this paper.
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Buildup of Speaking Skills in an Online Learning Community: A Network-Analytic Exploration | In this study, we explore peer-interaction effects in online networks on
speaking skill development. In particular, we present an evidence for gradual
buildup of skills in a small-group setting that has not been reported in the
literature. We introduce a novel dataset of six online communities consisting
of 158 participants focusing on improving their speaking skills. They
video-record speeches for 5 prompts in 10 days and exchange comments and
performance-ratings with their peers. We ask (i) whether the participants'
ratings are affected by their interaction patterns with peers, and (ii) whether
there is any gradual buildup of speaking skills in the communities towards
homogeneity. To analyze the data, we employ tools from the emerging field of
Graph Signal Processing (GSP). GSP enjoys a distinction from Social Network
Analysis in that the latter is concerned primarily with the connection
structures of graphs, while the former studies signals on top of graphs. We
study the performance ratings of the participants as graph signals atop
underlying interaction topologies. Total variation analysis of the graph
signals show that the participants' rating differences decrease with time
(slope=-0.04, p<0.01), while average ratings increase (slope=0.07,
p<0.05)--thereby gradually building up the ratings towards community-wide
homogeneity. We provide evidence for peer-influence through a prediction
formulation. Our consensus-based prediction model outperforms baseline
network-agnostic regression models by about 23% in predicting performance
ratings. This, in turn, shows that participants' ratings are affected by their
peers' ratings and the associated interaction patterns, corroborating previous
findings. Then, we formulate a consensus-based diffusion model that captures
these observations of peer-influence from our analyses.
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A Note on Kaldi's PLDA Implementation | Some explanations to Kaldi's PLDA implementation to make formula derivation
easier to catch.
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Breakdown of the Chiral Anomaly in Weyl Semimetals in a Strong Magnetic Field | The low-energy quasiparticles of Weyl semimetals are a condensed-matter
realization of the Weyl fermions introduced in relativistic field theory.
Chiral anomaly, the nonconservation of the chiral charge under parallel
electric and magnetic fields, is arguably the most important phenomenon of Weyl
semimetals and has been explained as an imbalance between the occupancies of
the gapless, zeroth Landau levels with opposite chiralities. This widely
accepted picture has served as the basis for subsequent studies. Here we report
the breakdown of the chiral anomaly in Weyl semimetals in a strong magnetic
field based on ab initio calculations. A sizable energy gap that depends
sensitively on the direction of the magnetic field may open up due to the
mixing of the zeroth Landau levels associated with the opposite-chirality Weyl
points that are away from each other in the Brillouin zone. Our study provides
a theoretical framework for understanding a wide range of phenomena closely
related to the chiral anomaly in topological semimetals, such as
magnetotransport, thermoelectric responses, and plasmons, to name a few.
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Predicting Auction Price of Vehicle License Plate with Deep Recurrent Neural Network | In Chinese societies, superstition is of paramount importance, and vehicle
license plates with desirable numbers can fetch very high prices in auctions.
Unlike other valuable items, license plates are not allocated an estimated
price before auction. I propose that the task of predicting plate prices can be
viewed as a natural language processing (NLP) task, as the value depends on the
meaning of each individual character on the plate and its semantics. I
construct a deep recurrent neural network (RNN) to predict the prices of
vehicle license plates in Hong Kong, based on the characters on a plate. I
demonstrate the importance of having a deep network and of retraining.
Evaluated on 13 years of historical auction prices, the deep RNN outperforms
previous models by a significant margin.
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Magnetic field--induced modification of selection rules for Rb D$_2$ line monitored by selective reflection from a vapor nanocell | Magnetic field-induced giant modification of the probabilities of five
transitions of $5S_{1/2}, F_g=2 \rightarrow 5P_{3/2}, F_e=4$ of $^{85}$Rb and
three transitions of $5S_{1/2}, F_g=1 \rightarrow 5P_{3/2}, F_e=3$ of $^{87}$Rb
forbidden by selection rules for zero magnetic field has been observed
experimentally and described theoretically for the first time. For the case of
excitation with circularly-polarized ($\sigma^+$) laser radiation, the
probability of $F_g=2, ~m_F=-2 \rightarrow F_e=4, ~m_F=-1$ transition becomes
the largest among the seventeen transitions of $^{85}$Rb $F_g=2 \rightarrow
F_e=1,2,3,4$ group, and the probability of $F_g=1,~m_F=-1 \rightarrow
F_e=3,~m_F=0$ transition becomes the largest among the nine transitions of
$^{87}$Rb $F_g=1 \rightarrow F_e=0,1,2,3$ group, in a wide range of magnetic
field 200 -- 1000 G. Complete frequency separation of individual Zeeman
components was obtained by implementation of derivative selective reflection
technique with a 300 nm-thick nanocell filled with Rb, allowing formation of
narrow optical resonances. Possible applications are addressed. The theoretical
model is perfectly consistent with the experimental results.
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An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs | In this work, we develop an adaptive, multivariate partitioning algorithm for
solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to
global optimality. This iterative algorithm primarily exploits the advantages
of piecewise polyhedral relaxation approaches via disjunctive formulations to
solve MINLPs to global optimality in contrast to the conventional spatial
branch-and-bound approaches. In order to maintain relatively small-scale
mixed-integer linear programs at every iteration of the algorithm, we
adaptively partition the variable domains appearing in the multi-linear terms.
We also provide proofs on convergence guarantees of the proposed algorithm to a
global solution. Further, we discuss a few algorithmic enhancements based on
the sequential bound-tightening procedure as a presolve step, where we observe
the importance of solving piecewise relaxations compared to basic convex
relaxations to speed-up the convergence of the algorithm to global optimality.
We demonstrate the effectiveness of our disjunctive formulations and the
algorithm on well-known benchmark problems (including Pooling and Blending
instances) from MINLPLib and compare with state-of-the-art global optimization
solvers. With this novel approach, we solve several large-scale instances which
are, in some cases, intractable by the global optimization solver. We also
shrink the best known optimality gap for one of the hard, generalized pooling
problem instance.
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Twists of quantum Borel algebras | We classify Drinfeld twists for the quantum Borel subalgebra u_q(b) in the
Frobenius-Lusztig kernel u_q(g), where g is a simple Lie algebra over C and q
an odd root of unity. More specifically, we show that alternating forms on the
character group of the group of grouplikes for u_q(b) generate all twists for
u_q(b), under a certain algebraic group action. This implies a simple
classification of Hopf algebras whose categories of representations are tensor
equivalent to that of u_q(b). We also show that cocycle twists for the
corresponding De Concini-Kac algebra are in bijection with alternating forms on
the aforementioned character group.
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Distributions and Statistical Power of Optimal Signal-Detection Methods In Finite Cases | In big data analysis for detecting rare and weak signals among $n$ features,
some grouping-test methods such as Higher Criticism test (HC), Berk-Jones test
(B-J), and $\phi$-divergence test share the similar asymptotical optimality
when $n \rightarrow \infty$. However, in practical data analysis $n$ is
frequently small and moderately large at most. In order to properly apply these
optimal tests and wisely choose them for practical studies, it is important to
know how to get the p-values and statistical power of them. To address this
problem in an even broader context, this paper provides analytical solutions
for a general family of goodness-of-fit (GOF) tests, which covers these optimal
tests. For any given i.i.d. and continuous distributions of the input test
statistics of the $n$ features, both p-value and statistical power of such a
GOF test can be calculated. By calculation we compared the finite-sample
performances of asymptotically optimal tests under the normal mixture
alternative. Results show that HC is the best choice when signals are rare,
while B-J is more robust over various signal patterns. In the application to a
real genome-wide association study, results illustrate that the p-value
calculation works well, and the optimal tests have potentials for detecting
novel disease genes with weak genetic effects. The calculations have been
implemented in an R package SetTest and published on the CRAN.
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Cubical-like geometry of quasi-median graphs and applications to geometric group theory | The class of quasi-median graphs is a generalisation of median graphs, or
equivalently of CAT(0) cube complexes. The purpose of this thesis is to
introduce these graphs in geometric group theory. In the first part of our
work, we extend the definition of hyperplanes from CAT(0) cube complexes, and
we show that the geometry of a quasi-median graph essentially reduces to the
combinatorics of its hyperplanes. In the second part, we exploit the specific
structure of the hyperplanes to state combination results. The main idea is
that if a group acts in a suitable way on a quasi-median graph so that
clique-stabilisers satisfy some non-positively curved property $\mathcal{P}$,
then the whole group must satisfy $\mathcal{P}$ as well. The properties we are
interested in are mainly (relative) hyperbolicity, (equivariant)
$\ell^p$-compressions, CAT(0)-ness and cubicality. In the third part, we apply
our general criteria to several classes of groups, including graph products,
Guba and Sapir's diagram products, some wreath products, and some graphs of
groups. Graph products are our most natural examples, where the link between
the group and its quasi-median graph is particularly strong and explicit; in
particular, we are able to determine precisely when a graph product is
relatively hyperbolic.
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Doubly Nested Network for Resource-Efficient Inference | We propose doubly nested network(DNNet) where all neurons represent their own
sub-models that solve the same task. Every sub-model is nested both layer-wise
and channel-wise. While nesting sub-models layer-wise is straight-forward with
deep-supervision as proposed in \cite{xie2015holistically}, channel-wise
nesting has not been explored in the literature to our best knowledge.
Channel-wise nesting is non-trivial as neurons between consecutive layers are
all connected to each other. In this work, we introduce a technique to solve
this problem by sorting channels topologically and connecting neurons
accordingly. For the purpose, channel-causal convolutions are used. Slicing
doubly nested network gives a working sub-network. The most notable application
of our proposed network structure with slicing operation is resource-efficient
inference. At test time, computing resources such as time and memory available
for running the prediction algorithm can significantly vary across devices and
applications. Given a budget constraint, we can slice the network accordingly
and use a sub-model for inference within budget, requiring no additional
computation such as training or fine-tuning after deployment. We demonstrate
the effectiveness of our approach in several practical scenarios of utilizing
available resource efficiently.
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Structural and bonding character of potassium-doped p-terphenyl superconductors | Recently, there is a series of reports by Wang et al. on the
superconductivity in K-doped p-terphenyl (KxC18H14) with the transition
temperatures range from 7 to 123 Kelvin. Identifying the structural and bonding
character is the key to understand the superconducting phases and the related
properties. Therefore we carried out an extensive study on the crystal
structures with different doping levels and investigate the thermodynamic
stability, structural, electronic, and magnetic properties by the
first-principles calculations. Our calculated structures capture most features
of the experimentally observed X-ray diffraction patterns. The K doping
concentration is constrained to within the range of 2 and 3. The obtained
formation energy indicates that the system at x = 2.5 is more stable. The
strong ionic bonding interaction is found in between K atoms and organic
molecules. The charge transfer accounts for the metallic feature of the doped
materials. For a small amount of charge transferred, the tilting force between
the two successive benzenes drives the system to stabilize at the
antiferromagnetic ground state, while the system exhibits non-magnetic behavior
with increasing charge transfer. The multiformity of band structures near the
Fermi level indicates that the driving force for superconductivity is
complicated.
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Influence of the Forward Difference Scheme for the Time Derivative on the Stability of Wave Equation Numerical Solution | Research on numerical stability of difference equations has been quite
intensive in the past century. The choice of difference schemes for the
derivative terms in these equations contributes to a wide range of the
stability analysis issues - one of which is how a chosen scheme may directly or
indirectly contribute to such stability. In the present paper, how far the
forward difference scheme for the time derivative in the wave equation
influences the stability of the equation numerical solution, is particularly
investigated. The stability analysis of the corresponding difference equation
involving four schemes, namely Lax's, central, forward, and rearward
differences, were carried out, and the resulting stability criteria were
compared. The results indicate that the instability of the solution of wave
equation is not always due to the forward difference scheme for the time
derivative. Rather, it is shown in this paper that the stability criterion is
still possible when the spatial derivative is represented by an appropriate
difference scheme. This sheds light on the degree of applicability of a
difference scheme for a hyperbolic equation.
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Uniqueness of the von Neumann continuous factor | For a division ring $D$, denote by $\mathcal M_D$ the $D$-ring obtained as
the completion of the direct limit $\varinjlim_n M_{2^n}(D)$ with respect to
the metric induced by its unique rank function. We prove that, for any
ultramatricial $D$-ring $\mathcal B$ and any non-discrete extremal pseudo-rank
function $N$ on $\mathcal B$, there is an isomorphism of $D$-rings
$\overline{\mathcal B} \cong \mathcal M_D$, where $\overline{\mathcal B}$
stands for the completion of $\mathcal B$ with respect to the pseudo-metric
induced by $N$. This generalizes a result of von Neumann. We also show a
corresponding uniqueness result for $*$-algebras over fields $F$ with positive
definite involution, where the algebra $\mathcal M_F$ is endowed with its
natural involution coming from the $*$-transpose involution on each of the
factors $M_{2^n}(F)$.
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A hybrid finite volume -- finite element method for bulk--surface coupled problems | The paper develops a hybrid method for solving a system of
advection--diffusion equations in a bulk domain coupled to advection--diffusion
equations on an embedded surface. A monotone nonlinear finite volume method for
equations posed in the bulk is combined with a trace finite element method for
equations posed on the surface. In our approach, the surface is not fitted by
the mesh and is allowed to cut through the background mesh in an arbitrary way.
Moreover, a triangulation of the surface into regular shaped elements is not
required. The background mesh is an octree grid with cubic cells. As an example
of an application, we consider the modeling of contaminant transport in
fractured porous media. One standard model leads to a coupled system of
advection--diffusion equations in a bulk (matrix) and along a surface
(fracture). A series of numerical experiments with both steady and unsteady
problems and different embedded geometries illustrate the numerical properties
of the hybrid approach. The method demonstrates great flexibility in handling
curvilinear or branching lower dimensional embedded structures.
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From Quenched Disorder to Continuous Time Random Walk | This work focuses on quantitative representation of transport in systems with
quenched disorder. Explicit mapping of the quenched trap model to continuous
time random walk is presented. Linear temporal transformation: $t\to
t/\Lambda^{1/\alpha}$ for transient process on translationally invariant
lattice, in the sub-diffusive regime, is sufficient for asymptotic mapping.
Exact form of the constant $\Lambda^{1/\alpha}$ is established. Disorder
averaged position probability density function for quenched trap model is
obtained and analytic expressions for the diffusion coefficient and drift are
provided.
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Network Flows that Solve Least Squares for Linear Equations | This paper presents a first-order {distributed continuous-time algorithm} for
computing the least-squares solution to a linear equation over networks. Given
the uniqueness of the solution, with nonintegrable and diminishing step size,
convergence results are provided for fixed graphs. The exact rate of
convergence is also established for various types of step size choices falling
into that category. For the case where non-unique solutions exist, convergence
to one such solution is proved for constantly connected switching graphs with
square integrable step size, and for uniformly jointly connected switching
graphs under the boundedness assumption on system states. Validation of the
results and illustration of the impact of step size on the convergence speed
are made using a few numerical examples.
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A Framework for Evaluating Model-Driven Self-adaptive Software Systems | In the last few years, Model Driven Development (MDD), Component-based
Software Development (CBSD), and context-oriented software have become
interesting alternatives for the design and construction of self-adaptive
software systems. In general, the ultimate goal of these technologies is to be
able to reduce development costs and effort, while improving the modularity,
flexibility, adaptability, and reliability of software systems. An analysis of
these technologies shows them all to include the principle of the separation of
concerns, and their further integration is a key factor to obtaining
high-quality and self-adaptable software systems. Each technology identifies
different concerns and deals with them separately in order to specify the
design of the self-adaptive applications, and, at the same time, support
software with adaptability and context-awareness. This research studies the
development methodologies that employ the principles of model-driven
development in building self-adaptive software systems. To this aim, this
article proposes an evaluation framework for analysing and evaluating the
features of model-driven approaches and their ability to support software with
self-adaptability and dependability in highly dynamic contextual environment.
Such evaluation framework can facilitate the software developers on selecting a
development methodology that suits their software requirements and reduces the
development effort of building self-adaptive software systems. This study
highlights the major drawbacks of the propped model-driven approaches in the
related works, and emphasise on considering the volatile aspects of
self-adaptive software in the analysis, design and implementation phases of the
development methodologies. In addition, we argue that the development
methodologies should leave the selection of modelling languages and modelling
tools to the software developers.
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Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems | In this article we study optimal control problems for systems that are affine
with respect to some of the control variables and nonlinear in relation to the
others. We consider finitely many equality and inequality constraints on the
initial and final values of the state. We investigate singular optimal
solutions for this class of problems, for which we obtain second order
necessary and sufficient conditions for weak optimality in integral form. We
also derive Goh pointwise necessary optimality conditions. We show an example
to illustrate the results.
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Bipartite Envy-Free Matching | Bipartite Envy-Free Matching (BEFM) is a relaxation of perfect matching. In a
bipartite graph with parts X and Y, a BEFM is a matching of some vertices in X
to some vertices in Y, such that each unmatched vertex in X is not adjacent to
any matched vertex in Y (so the unmatched vertices do not "envy" the matched
ones). The empty matching is always a BEFM. This paper presents sufficient and
necessary conditions for the existence of a non-empty BEFM. These conditions
are based on cardinality of neighbor-sets, similarly to Hall's condition for
the existence of a perfect matching. The conditions can be verified in
polynomial time, and in case they are satisfied, a non-empty BEFM can be found
by a polynomial-time algorithm. The paper presents some applications of BEFM as
a subroutine in fair division algorithms.
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Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing | Off-diagonal Aubry-André (AA) model has recently attracted a great deal
of attention as they provide condensed matter realization of topological
phases. We numerically study a generalized off-diagonal AA model with p-wave
superfluid pairing in the presence of both commensurate and incommensurate
hopping modulations. The phase diagram as functions of the modulation strength
of incommensurate hopping and the strength of the p-wave pairing is obtained by
using the multifractal analysis. We show that with the appearance of the p-wave
pairing, the system exhibits mobility-edge phases and critical phases with
various number of topologically protected zero-energy modes. Predicted
topological nature of these exotic phases can be realized in a cold atomic
system of incommensurate bichromatic optical lattice with induced p-wave
superfluid pairing by using a Raman laser in proximity to a molecular
Bose-Einstein condensation.
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Around Average Behavior: 3-lambda Network Model | The analysis of networks affects the research of many real phenomena. The
complex network structure can be viewed as a network's state at the time of the
analysis or as a result of the process through which the network arises.
Research activities focus on both and, thanks to them, we know not only many
measurable properties of networks but also the essence of some phenomena that
occur during the evolution of networks. One typical research area is the
analysis of co-authorship networks and their evolution. In our paper, the
analysis of one real-world co-authorship network and inspiration from existing
models form the basis of the hypothesis from which we derive new 3-lambda
network model. This hypothesis works with the assumption that regular behavior
of nodes revolves around an average. However, some anomalies may occur. The
3-lambda model is stochastic and uses the three parameters associated with the
average behavior of the nodes. The growth of the network based on this model
assumes that one step of the growth is an interaction in which both new and
existing nodes are participating. In the paper we present the results of the
analysis of a co-authorship network and formulate a hypothesis and a model
based on this hypothesis. Later in the paper, we examine the outputs from the
network generator based on the 3-lambda model and show that generated networks
have characteristics known from the environment of real-world networks.
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Hierarchical star formation across the grand design spiral NGC1566 | We investigate how star formation is spatially organized in the grand-design
spiral NGC 1566 from deep HST photometry with the Legacy ExtraGalactic UV
Survey (LEGUS). Our contour-based clustering analysis reveals 890 distinct
stellar conglomerations at various levels of significance. These star-forming
complexes are organized in a hierarchical fashion with the larger congregations
consisting of smaller structures, which themselves fragment into even smaller
and more compact stellar groupings. Their size distribution, covering a wide
range in length-scales, shows a power-law as expected from scale-free
processes. We explain this shape with a simple "fragmentation and enrichment"
model. The hierarchical morphology of the complexes is confirmed by their
mass--size relation which can be represented by a power-law with a fractional
exponent, analogous to that determined for fractal molecular clouds. The
surface stellar density distribution of the complexes shows a log-normal shape
similar to that for supersonic non-gravitating turbulent gas. Between 50 and 65
per cent of the recently-formed stars, as well as about 90 per cent of the
young star clusters, are found inside the stellar complexes, located along the
spiral arms. We find an age-difference between young stars inside the complexes
and those in their direct vicinity in the arms of at least 10 Myr. This
timescale may relate to the minimum time for stellar evaporation, although we
cannot exclude the in situ formation of stars. As expected, star formation
preferentially occurs in spiral arms. Our findings reveal turbulent-driven
hierarchical star formation along the arms of a grand-design galaxy.
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Informed Asymptotically Optimal Anytime Search | Path planning in robotics often requires finding high-quality solutions to
continuously valued and/or high-dimensional problems. These problems are
challenging and most planning algorithms instead solve simplified
approximations. Popular approximations include graphs and random samples, as
respectively used by informed graph-based searches and anytime sampling-based
planners. Informed graph-based searches, such as A*, traditionally use
heuristics to search a priori graphs in order of potential solution quality.
This makes their search efficient but leaves their performance dependent on the
chosen approximation. If its resolution is too low then they may not find a
(suitable) solution but if it is too high then they may take a prohibitively
long time to do so. Anytime sampling-based planners, such as RRT*,
traditionally use random sampling to approximate the problem domain
incrementally. This allows them to increase resolution until a suitable
solution is found but makes their search dependent on the order of
approximation. Arbitrary sequences of random samples expand the approximation
in every direction and fill the problem domain but may be prohibitively
inefficient at containing a solution. This paper unifies and extends these two
approaches to develop Batch Informed Trees (BIT*), an informed, anytime
sampling-based planner. BIT* solves continuous path planning problems
efficiently by using sampling and heuristics to alternately approximate and
search the problem domain. Its search is ordered by potential solution quality,
as in A*, and its approximation improves indefinitely with additional
computational time, as in RRT*. It is shown analytically to be almost-surely
asymptotically optimal and experimentally to outperform existing sampling-based
planners, especially on high-dimensional planning problems.
| 1 | 0 | 0 | 0 | 0 | 0 |
Certifying coloring algorithms for graphs without long induced paths | Let $P_k$ be a path, $C_k$ a cycle on $k$ vertices, and $K_{k,k}$ a complete
bipartite graph with $k$ vertices on each side of the bipartition. We prove
that (1) for any integers $k, t>0$ and a graph $H$ there are finitely many
subgraph minimal graphs with no induced $P_k$ and $K_{t,t}$ that are not
$H$-colorable and (2) for any integer $k>4$ there are finitely many subgraph
minimal graphs with no induced $P_k$ that are not $C_{k-2}$-colorable.
The former generalizes the result of Hell and Huang [Complexity of coloring
graphs without paths and cycles, Discrete Appl. Math. 216: 211--232 (2017)] and
the latter extends a result of Bruce, Hoang, and Sawada [A certifying algorithm
for 3-colorability of $P_5$-Free Graphs, ISAAC 2009: 594--604]. Both our
results lead to polynomial-time certifying algorithms for the corresponding
coloring problems.
| 1 | 0 | 0 | 0 | 0 | 0 |
Efficient Estimation for Dimension Reduction with Censored Data | We propose a general index model for survival data, which generalizes many
commonly used semiparametric survival models and belongs to the framework of
dimension reduction. Using a combination of geometric approach in
semiparametrics and martingale treatment in survival data analysis, we devise
estimation procedures that are feasible and do not require
covariate-independent censoring as assumed in many dimension reduction methods
for censored survival data. We establish the root-$n$ consistency and
asymptotic normality of the proposed estimators and derive the most efficient
estimator in this class for the general index model. Numerical experiments are
carried out to demonstrate the empirical performance of the proposed estimators
and an application to an AIDS data further illustrates the usefulness of the
work.
| 0 | 0 | 1 | 1 | 0 | 0 |
Analysis of error control in large scale two-stage multiple hypothesis testing | When dealing with the problem of simultaneously testing a large number of
null hypotheses, a natural testing strategy is to first reduce the number of
tested hypotheses by some selection (screening or filtering) process, and then
to simultaneously test the selected hypotheses. The main advantage of this
strategy is to greatly reduce the severe effect of high dimensions. However,
the first screening or selection stage must be properly accounted for in order
to maintain some type of error control. In this paper, we will introduce a
selection rule based on a selection statistic that is independent of the test
statistic when the tested hypothesis is true. Combining this selection rule and
the conventional Bonferroni procedure, we can develop a powerful and valid
two-stage procedure. The introduced procedure has several nice properties: (i)
it completely removes the selection effect; (ii) it reduces the multiplicity
effect; (iii) it does not "waste" data while carrying out both selection and
testing. Asymptotic power analysis and simulation studies illustrate that this
proposed method can provide higher power compared to usual multiple testing
methods while controlling the Type 1 error rate. Optimal selection thresholds
are also derived based on our asymptotic analysis.
| 0 | 0 | 1 | 1 | 0 | 0 |
Subdifferential characterization of probability functions under Gaussian distribution | Probability functions figure prominently in optimization problems of
engineering. They may be nonsmooth even if all input data are smooth.This fact
motivates the consideration of subdifferentials for such typically just
continuous functions. The aim of this paper is to provide subdifferential
formulae in the case of Gaussian distributions for possibly
infinite-dimensional decision variables and nonsmooth (locally Lipschitzian)
input data. These formulae are based on the spheric-radial decomposition of
Gaussian random vectors on the one hand and on a cone of directions of moderate
growth on the other. By successively adding additional hypotheses, conditions
are satisfied under which the probability function is locally Lipschitzian or
even differentiable.
| 0 | 0 | 1 | 0 | 0 | 0 |
XES Tensorflow - Process Prediction using the Tensorflow Deep-Learning Framework | Predicting the next activity of a running process is an important aspect of
process management. Recently, artificial neural networks, so called
deep-learning approaches, have been proposed to address this challenge. This
demo paper describes a software application that applies the Tensorflow
deep-learning framework to process prediction. The software application reads
industry-standard XES files for training and presents the user with an
easy-to-use graphical user interface for both training and prediction. The
system provides several improvements over earlier work. This demo paper focuses
on the software implementation and describes the architecture and user
interface.
| 1 | 0 | 0 | 0 | 0 | 0 |
EPTL - A temporal logic for weakly consistent systems | The high availability and scalability of weakly-consistent systems attracts
system designers. Yet, writing correct application code for this type of
systems is difficult; even how to specify the intended behavior of such systems
is still an open question. There has not been established any standard method
to specify the intended dynamic behavior of a weakly consistent system. There
exist specifications of various consistency models for distributed and
concurrent systems; and the semantics of replicated datatypes like CRDTs have
been specified in axiomatic and operational models based on visibility
relations.
In this paper, we present a temporal logic, EPTL, that is tailored to specify
properties of weakly consistent systems. In contrast to LTL and CTL, EPTL takes
into account that operations of weakly consistent systems are in many cases not
serializable and have to be treated respectively to capture the behavior. We
embed our temporal logic in Isabelle/HOL and can thereby leverage strong
semi-automatic proving capabilities.
| 1 | 0 | 0 | 0 | 0 | 0 |
An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4x4 Lax pair on the half-line | We investigate the initial-boundary value problem for the integrable spin-1
Gross-Pitaevskii (GP) equations with a 4x4 Lax pair on the half-line. The
solution of this system can be obtained in terms of the solution of a 4x4
matrix Riemann-Hilbert (RH) problem formulated in the complex k-plane. The
relevant jump matrices of the RH problem can be explicitly found using the two
spectral functions s(k) and S(k), which can be defined by the initial data, the
Dirichlet-Neumann boundary data at x=0. The global relation is established
between the two dependent spectral functions. The general mappings between
Dirichlet and Neumann boundary values are analyzed in terms of the global
relation.
| 0 | 1 | 1 | 0 | 0 | 0 |
4-DoF Tracking for Robot Fine Manipulation Tasks | This paper presents two visual trackers from the different paradigms of
learning and registration based tracking and evaluates their application in
image based visual servoing. They can track object motion with four degrees of
freedom (DoF) which, as we will show here, is sufficient for many fine
manipulation tasks. One of these trackers is a newly developed learning based
tracker that relies on learning discriminative correlation filters while the
other is a refinement of a recent 8 DoF RANSAC based tracker adapted with a new
appearance model for tracking 4 DoF motion.
Both trackers are shown to provide superior performance to several state of
the art trackers on an existing dataset for manipulation tasks. Further, a new
dataset with challenging sequences for fine manipulation tasks captured from
robot mounted eye-in-hand (EIH) cameras is also presented. These sequences have
a variety of challenges encountered during real tasks including jittery camera
movement, motion blur, drastic scale changes and partial occlusions.
Quantitative and qualitative results on these sequences are used to show that
these two trackers are robust to failures while providing high precision that
makes them suitable for such fine manipulation tasks.
| 1 | 0 | 0 | 0 | 0 | 0 |
Absence of chaos in Digital Memcomputing Machines with solutions | Digital memcomputing machines (DMMs) are non-linear dynamical systems
designed so that their equilibrium points are solutions of the Boolean problem
they solve. In a previous work [Chaos 27, 023107 (2017)] it was argued that
when DMMs support solutions of the associated Boolean problem then strange
attractors cannot coexist with such equilibria. In this work, we demonstrate
such conjecture. In particular, we show that both topological transitivity and
the strongest property of topological mixing are inconsistent with the point
dissipative property of DMMs when equilibrium points are present. This is true
for both the whole phase space and the global attractor. Absence of topological
transitivity is enough to imply absence of chaotic behavior. In a similar vein,
we prove that if DMMs do not have equilibrium points, the only attractors
present are invariant tori/periodic orbits with periods that may possibly
increase with system size (quasi-attractors).
| 1 | 1 | 0 | 0 | 0 | 0 |
New ideas for tests of Lorentz invariance with atomic systems | We describe a broadly applicable experimental proposal to search for the
violation of local Lorentz invariance (LLI) with atomic systems. The new scheme
uses dynamic decoupling and can be implemented in current atomic clocks
experiments, both with single ions and arrays of neutral atoms. Moreover, the
scheme can be performed on systems with no optical transitions, and therefore
it is also applicable to highly charged ions which exhibit particularly high
sensitivity to Lorentz invariance violation. We show the results of an
experiment measuring the expected signal of this proposal using a two-ion
crystal of $^{88}$Sr$^+$ ions. We also carry out a systematic study of the
sensitivity of highly charged ions to LLI to identify the best candidates for
the LLI tests.
| 0 | 1 | 0 | 0 | 0 | 0 |
Fine-resolution analysis of exoplanetary distributions by wavelets: hints of an overshooting iceline accumulation | We investigate 1D exoplanetary distributions using a novel analysis algorithm
based on the continuous wavelet transform. The analysis pipeline includes an
estimation of the wavelet transform of the probability density function
(p.d.f.) without pre-binning, use of optimized wavelets, a rigorous
significance testing of the patterns revealed in the p.d.f., and an optimized
minimum-noise reconstruction of the p.d.f. via matching pursuit iterations.
In the distribution of orbital periods, $P$, our analysis revealed a narrow
subfamily of exoplanets within the broad family of "warm jupiters", or massive
giants with $P\gtrsim 300$~d, which are often deemed to be related with the
iceline accumulation in a protoplanetary disk. We detected a p.d.f. pattern
that represents an upturn followed by an overshooting peak spanning $P\sim
300-600$~d, right beyond the "period valley". It is separated from the other
planets by p.d.f. concavities from both sides. It has at least two-sigma
significance.
In the distribution of planet radii, $R$, and using the California Kepler
Survey sample properly cleaned, we confirm the hints of a bimodality with two
peaks about $R=1.3 R_\oplus$ and $R=2.4 R_\oplus$, and the "evaporation valley"
between them. However, we obtain just a modest significance for this pattern,
two-sigma only at the best. Besides, our follow-up application of the Hartigan
& Hartigan dip test for unimodality returns $3$ per cent false alarm
probability (merely $2.2$-sigma significance), contrary to $0.14$ per cent (or
$3.2$-sigma), as claimed by Fulton et al. (2017).
| 0 | 1 | 0 | 0 | 0 | 0 |
Small sets in dense pairs | Let $\widetilde{\mathcal M}=\langle \mathcal M, P\rangle$ be an expansion of
an o-minimal structure $\mathcal M$ by a dense set $P\subseteq M$, such that
three tameness conditions hold. We prove that the induced structure on $P$ by
$\mathcal M$ eliminates imaginaries. As a corollary, we obtain that every small
set $X$ definable in $\widetilde{\mathcal M}$ can be definably embedded into
some $P^l$, uniformly in parameters, settling a question from [10]. We verify
the tameness conditions in three examples: dense pairs of real closed fields,
expansions of $\mathcal M$ by a dense independent set, and expansions by a
dense divisible multiplicative group with the Mann property. Along the way, we
point out a gap in the proof of a relevant elimination of imaginaries result in
Wencel [17]. The above results are in contrast to recent literature, as it is
known in general that $\widetilde{\mathcal M}$ does not eliminate imaginaries,
and neither it nor the induced structure on $P$ admits definable Skolem
functions.
| 0 | 0 | 1 | 0 | 0 | 0 |
Meta-Learning MCMC Proposals | Effective implementations of sampling-based probabilistic inference often
require manually constructed, model-specific proposals. Inspired by recent
progresses in meta-learning for training learning agents that can generalize to
unseen environments, we propose a meta-learning approach to building effective
and generalizable MCMC proposals. We parametrize the proposal as a neural
network to provide fast approximations to block Gibbs conditionals. The learned
neural proposals generalize to occurrences of common structural motifs across
different models, allowing for the construction of a library of learned
inference primitives that can accelerate inference on unseen models with no
model-specific training required. We explore several applications including
open-universe Gaussian mixture models, in which our learned proposals
outperform a hand-tuned sampler, and a real-world named entity recognition
task, in which our sampler yields higher final F1 scores than classical
single-site Gibbs sampling.
| 1 | 0 | 0 | 1 | 0 | 0 |
Putting Self-Supervised Token Embedding on the Tables | Information distribution by electronic messages is a privileged means of
transmission for many businesses and individuals, often under the form of
plain-text tables. As their number grows, it becomes necessary to use an
algorithm to extract text and numbers instead of a human. Usual methods are
focused on regular expressions or on a strict structure in the data, but are
not efficient when we have many variations, fuzzy structure or implicit labels.
In this paper we introduce SC2T, a totally self-supervised model for
constructing vector representations of tokens in semi-structured messages by
using characters and context levels that address these issues. It can then be
used for an unsupervised labeling of tokens, or be the basis for a
semi-supervised information extraction system.
| 1 | 0 | 0 | 0 | 0 | 0 |
Enhanced ferromagnetic transition temperature induced by a microscopic structural rearrangement in the diluted magnetic semiconductor Ge$_{1-x}$Mn$_{x}$Te | The correlation between magnetic properties and microscopic structural
aspects in the diluted magnetic semiconductor Ge$_{1-x}$Mn$_{x}$Te is
investigated by x-ray diffraction and magnetization as a function of the Mn
concentration $x$. The occurrence of high ferromagnetic-transition temperatures
in the rhombohedrally distorted phase of slowly-cooled Ge$_{1-x}$Mn$_{x}$Te is
shown to be directly correlated with the formation and coexistence of
strongly-distorted Mn-poor and weakly-distorted Mn-rich regions. It is
demonstrated that the weakly-distorted phase fraction is responsible for the
occurrence of high-transition temperatures in Ge$_{1-x}$Mn$_{x}$Te. When the Mn
concentration becomes larger, the Mn-rich regions start to switch into the
undistorted cubic structure, and the transition temperature is suppressed
concurrently. By identifying suitable annealing conditions, we successfully
increased the transition temperature to above 200 K for Mn concentrations close
to the cubic phase. Structural data indicate that the weakly-distorted phase
fraction can be restored at the expense of the cubic regions upon the
enhancement of the transition temperature, clearly establishing the direct link
between high-transition temperatures and the weakly-distorted Mn-rich phase
fraction.
| 0 | 1 | 0 | 0 | 0 | 0 |
Getting the public involved in Quantum Error Correction | The Decodoku project seeks to let users get hands-on with cutting-edge
quantum research through a set of simple puzzle games. The design of these
games is explicitly based on the problem of decoding qudit variants of surface
codes. This problem is presented such that it can be tackled by players with no
prior knowledge of quantum information theory, or any other high-level physics
or mathematics. Methods devised by the players to solve the puzzles can then
directly be incorporated into decoding algorithms for quantum computation. In
this paper we give a brief overview of the novel decoding methods devised by
players, and provide short postmortem for Decodoku v1.0-v4.1.
| 0 | 1 | 0 | 0 | 0 | 0 |
Courcelle's Theorem Made Dynamic | Dynamic complexity is concerned with updating the output of a problem when
the input is slightly changed. We study the dynamic complexity of model
checking a fixed monadic second-order formula over evolving subgraphs of a
fixed maximal graph having bounded tree-width; here the subgraph evolves by
losing or gaining edges (from the maximal graph). We show that this problem is
in DynFO (with LOGSPACE precomputation), via a reduction to a Dyck reachability
problem on an acyclic automaton.
| 1 | 0 | 0 | 0 | 0 | 0 |
PorePy: An Open-Source Simulation Tool for Flow and Transport in Deformable Fractured Rocks | Fractures are ubiquitous in the subsurface and strongly affect flow and
deformation. The physical shape of the fractures, they are long and thin
objects, puts strong limitations on how the effect of this dynamics can be
incorporated into standard reservoir simulation tools. This paper reports the
development of an open-source software framework, termed PorePy, which is aimed
at simulation of flow and transport in three-dimensional fractured reservoirs,
as well as deformation of the reservoir due to shearing along fracture and
fault planes. Starting from a description of fractures as polygons embedded in
a 3D domain, PorePy provides semi-automatic gridding to construct a
discrete-fracture-matrix model, which forms the basis for subsequent
simulations. PorePy allows for flow and transport in all lower-dimensional
objects, including planes (2D) representing fractures, and lines (1D) and
points (0D), representing fracture intersections. Interaction between processes
in neighboring domains of different dimension is implemented as a sequence of
couplings of objects one dimension apart. This readily allows for handling of
complex fracture geometries compared to capabilities of existing software. In
addition to flow and transport, PorePy provides models for rock mechanics,
poro-elasticity and coupling with fracture deformation models. The software is
fully open, and can serve as a framework for transparency and reproducibility
of simulations. We describe the design principles of PorePy from a user
perspective, with focus on possibilities within gridding, covered physical
processes and available discretizations. The power of the framework is
illustrated with two sets of simulations; involving respectively coupled flow
and transport in a fractured porous medium, and low-pressure stimulation of a
geothermal reservoir.
| 1 | 1 | 0 | 0 | 0 | 0 |
Second-grade fluids in curved pipes | This paper is concerned with the application of finite element methods to
obtain solutions for steady fully developed second-grade flows in a curved pipe
of circular cross-section and arbitrary curvature ratio, under a given axial
pressure gradient. The qualitative and quantitative behavior of the secondary
flows is analyzed with respect to inertia and viscoelasticity.
| 0 | 1 | 1 | 0 | 0 | 0 |
Designing nearly tight window for improving time-frequency masking | Many audio signal processing methods are formulated in the time-frequency
(T-F) domain which is obtained by the short-time Fourier transform (STFT). The
property of STFT is fully characterized by window function, and thus designing
a better window is important for improving the performance of the processing
especially when a less redundant T-F representation is desirable. While many
window functions have been proposed in the literature, they are designed to
have a good frequency response for analysis, which may not perform well in
terms of signal processing. The window design must take the effect of the
reconstruction (from the T-F domain into the time domain) into account for
improving the performance. In this paper, an optimization-based design method
of a nearly tight window is proposed to obtain a window performing well for the
T-F domain signal processing.
| 1 | 0 | 0 | 0 | 0 | 0 |
Asymptotic Properties of Recursive Maximum Likelihood Estimation in Non-Linear State-Space Models | Using stochastic gradient search and the optimal filter derivative, it is
possible to perform recursive (i.e., online) maximum likelihood estimation in a
non-linear state-space model. As the optimal filter and its derivative are
analytically intractable for such a model, they need to be approximated
numerically. In [Poyiadjis, Doucet and Singh, Biometrika 2018], a recursive
maximum likelihood algorithm based on a particle approximation to the optimal
filter derivative has been proposed and studied through numerical simulations.
Here, this algorithm and its asymptotic behavior are analyzed theoretically. We
show that the algorithm accurately estimates maxima to the underlying (average)
log-likelihood when the number of particles is sufficiently large. We also
derive (relatively) tight bounds on the estimation error. The obtained results
hold under (relatively) mild conditions and cover several classes of non-linear
state-space models met in practice.
| 0 | 0 | 0 | 1 | 0 | 0 |
A Fast Integrated Planning and Control Framework for Autonomous Driving via Imitation Learning | For safe and efficient planning and control in autonomous driving, we need a
driving policy which can achieve desirable driving quality in long-term horizon
with guaranteed safety and feasibility. Optimization-based approaches, such as
Model Predictive Control (MPC), can provide such optimal policies, but their
computational complexity is generally unacceptable for real-time
implementation. To address this problem, we propose a fast integrated planning
and control framework that combines learning- and optimization-based approaches
in a two-layer hierarchical structure. The first layer, defined as the "policy
layer", is established by a neural network which learns the long-term optimal
driving policy generated by MPC. The second layer, called the "execution
layer", is a short-term optimization-based controller that tracks the reference
trajecotries given by the "policy layer" with guaranteed short-term safety and
feasibility. Moreover, with efficient and highly-representative features, a
small-size neural network is sufficient in the "policy layer" to handle many
complicated driving scenarios. This renders online imitation learning with
Dataset Aggregation (DAgger) so that the performance of the "policy layer" can
be improved rapidly and continuously online. Several exampled driving scenarios
are demonstrated to verify the effectiveness and efficiency of the proposed
framework.
| 1 | 0 | 0 | 0 | 0 | 0 |
Microservices in Practice: A Survey Study | Microservices architectures have become largely popular in the last years.
However, we still lack empirical evidence about the use of microservices and
the practices followed by practitioners. Thereupon, in this paper, we report
the results of a survey with 122 professionals who work with microservices. We
report how the industry is using this architectural style and whether the
perception of practitioners regarding the advantages and challenges of
microservices is according to the literature.
| 1 | 0 | 0 | 0 | 0 | 0 |
Predicted novel insulating electride compound between alkali metals lithium and sodium under high pressure | The application of high pressure can fundamentally modify the crystalline and
electronic structures of elements as well as their chemical reactivity, which
could lead to the formation of novel materials. Here, we explore the reactivity
of lithium with sodium under high pressure, using a swarm structure searching
techniques combined with first-principles calculations, which identify a
thermodynamically stable LiNa compound adopting an orthorhombic oP8 phase at
pressure above 355 GPa. The formation of LiNa may be a consequence of strong
concentration of electrons transfer from the lithium and the sodium atoms into
the interstitial sites, which also leads to opening a relatively wide band gap
for LiNa-op8. This is substantially different from the picture that share or
exchange electrons in common compounds and alloys. In addition, lattice-dynamic
calculations indicate that LiNa-op8 remains dynamically stable when pressure
decompresses down to 70 GPa.
| 0 | 1 | 0 | 0 | 0 | 0 |
The relationship between $k$-forcing and $k$-power domination | Zero forcing and power domination are iterative processes on graphs where an
initial set of vertices are observed, and additional vertices become observed
based on some rules. In both cases, the goal is to eventually observe the
entire graph using the fewest number of initial vertices. Chang et al.
introduced $k$-power domination in [Generalized power domination in graphs,
{\it Discrete Applied Math.} 160 (2012) 1691-1698] as a generalization of power
domination and standard graph domination. Independently, Amos et al. defined
$k$-forcing in [Upper bounds on the $k$-forcing number of a graph, {\it
Discrete Applied Math.} 181 (2015) 1-10] to generalize zero forcing. In this
paper, we combine the study of $k$-forcing and $k$-power domination, providing
a new approach to analyze both processes. We give a relationship between the
$k$-forcing and the $k$-power domination numbers of a graph that bounds one in
terms of the other. We also obtain results using the contraction of subgraphs
that allow the parallel computation of $k$-forcing and $k$-power dominating
sets.
| 0 | 0 | 1 | 0 | 0 | 0 |
The transition matrix between the Specht and web bases is unipotent with additional vanishing entries | We compare two important bases of an irreducible representation of the
symmetric group: the web basis and the Specht basis. The web basis has its
roots in the Temperley-Lieb algebra and knot-theoretic considerations. The
Specht basis is a classic algebraic and combinatorial construction of symmetric
group representations which arises in this context through the geometry of
varieties called Springer fibers. We describe a graph that encapsulates
combinatorial relations between each of these bases, prove that there is a
unique way (up to scaling) to map the Specht basis into the web representation,
and use this to recover a result of Garsia-McLarnan that the transition matrix
between the Specht and web bases is upper-triangular with ones along the
diagonal. We then strengthen their result to prove vanishing of certain
additional entries unless a nesting condition on webs is satisfied. In fact we
conjecture that the entries of the transition matrix are nonnegative and are
nonzero precisely when certain directed paths exist in the web graph.
| 0 | 0 | 1 | 0 | 0 | 0 |
Robotic Wireless Sensor Networks | In this chapter, we present a literature survey of an emerging, cutting-edge,
and multi-disciplinary field of research at the intersection of Robotics and
Wireless Sensor Networks (WSN) which we refer to as Robotic Wireless Sensor
Networks (RWSN). We define a RWSN as an autonomous networked multi-robot system
that aims to achieve certain sensing goals while meeting and maintaining
certain communication performance requirements, through cooperative control,
learning and adaptation. While both of the component areas, i.e., Robotics and
WSN, are very well-known and well-explored, there exist a whole set of new
opportunities and research directions at the intersection of these two fields
which are relatively or even completely unexplored. One such example would be
the use of a set of robotic routers to set up a temporary communication path
between a sender and a receiver that uses the controlled mobility to the
advantage of packet routing. We find that there exist only a limited number of
articles to be directly categorized as RWSN related works whereas there exist a
range of articles in the robotics and the WSN literature that are also relevant
to this new field of research. To connect the dots, we first identify the core
problems and research trends related to RWSN such as connectivity,
localization, routing, and robust flow of information. Next, we classify the
existing research on RWSN as well as the relevant state-of-the-arts from
robotics and WSN community according to the problems and trends identified in
the first step. Lastly, we analyze what is missing in the existing literature,
and identify topics that require more research attention in the future.
| 1 | 0 | 0 | 0 | 0 | 0 |
Using Mode Connectivity for Loss Landscape Analysis | Mode connectivity is a recently introduced frame- work that empirically
establishes the connected- ness of minima by finding a high accuracy curve
between two independently trained models. To investigate the limits of this
setup, we examine the efficacy of this technique in extreme cases where the
input models are trained or initialized differently. We find that the procedure
is resilient to such changes. Given this finding, we propose using the
framework for analyzing loss surfaces and training trajectories more generally,
and in this direction, study SGD with cosine annealing and restarts (SGDR). We
report that while SGDR moves over barriers in its trajectory, propositions
claiming that it converges to and escapes from multiple local minima are not
substantiated by our empirical results.
| 0 | 0 | 0 | 1 | 0 | 0 |
Lifelong Generative Modeling | Lifelong learning is the problem of learning multiple consecutive tasks in a
sequential manner where knowledge gained from previous tasks is retained and
used for future learning. It is essential towards the development of
intelligent machines that can adapt to their surroundings. In this work we
focus on a lifelong learning approach to generative modeling where we
continuously incorporate newly observed distributions into our learnt model. We
do so through a student-teacher Variational Autoencoder architecture which
allows us to learn and preserve all the distributions seen so far without the
need to retain the past data nor the past models. Through the introduction of a
novel cross-model regularizer, inspired by a Bayesian update rule, the student
model leverages the information learnt by the teacher, which acts as a summary
of everything seen till now. The regularizer has the additional benefit of
reducing the effect of catastrophic interference that appears when we learn
over sequences of distributions. We demonstrate its efficacy in learning
sequentially observed distributions as well as its ability to learn a common
latent representation across a complex transfer learning scenario.
| 1 | 0 | 0 | 1 | 0 | 0 |
Finding Root Causes of Floating Point Error with Herbgrind | Floating-point arithmetic plays a central role in science, engineering, and
finance by enabling developers to approximate real arithmetic. To address
numerical issues in large floating-point applications, developers must identify
root causes, which is difficult because floating-point errors are generally
non-local, non-compositional, and non-uniform.
This paper presents Herbgrind, a tool to help developers identify and address
root causes in numerical code written in low-level C/C++ and Fortran. Herbgrind
dynamically tracks dependencies between operations and program outputs to avoid
false positives and abstracts erroneous computations to a simplified program
fragment whose improvement can reduce output error. We perform several case
studies applying Herbgrind to large, expert-crafted numerical programs and show
that it scales to applications spanning hundreds of thousands of lines,
correctly handling the low-level details of modern floating point hardware and
mathematical libraries, and tracking error across function boundaries and
through the heap.
| 1 | 0 | 0 | 0 | 0 | 0 |
Catalog of Candidates for Quasars at 3 < z < 5.5 Selected among X-Ray Sources from the 3XMM-DR4 Survey of the XMM-Newton Observatory | We have compiled a catalog of 903 candidates for type 1 quasars at redshifts
3<z<5.5 selected among the X-ray sources of the serendipitous XMM-Newton survey
presented in the 3XMM-DR4 catalog (the median X-ray flux is 5x10^{-15}
erg/s/cm^2 the 0.5-2 keV energy band) and located at high Galactic latitudes
>20 deg in Sloan Digital Sky Survey (SDSS) fields with a total area of about
300 deg^2. Photometric SDSS data as well infrared 2MASS and WISE data were used
to select the objects. We selected the point sources from the photometric SDSS
catalog with a magnitude error Delta z<0.2 and a color i-z<0.6 (to first
eliminate the M-type stars). For the selected sources, we have calculated the
dependences chi^2(z) for various spectral templates from the library that we
compiled for these purposes using the EAZY software. Based on these data, we
have rejected the objects whose spectral energy distributions are better
described by the templates of stars at z=0 and obtained a sample of quasars
with photometric redshift estimates 2.75<zphot<5.5. The selection completeness
of known quasars at z>3 in the investigated fields is shown to be about 80%.
The normalized median absolute deviation is 0.07, while the outlier fraction is
eta= 9. The number of objects per unit area in our sample exceeds the number of
quasars in the spectroscopic SDSS sample at the same redshifts approximately by
a factor of 1.5. The subsequent spectroscopic testing of the redshifts of our
selected candidates for quasars at 3<z<5.5 will allow the purity of this sample
to be estimated more accurately.
| 0 | 1 | 0 | 0 | 0 | 0 |
The Theta Number of Simplicial Complexes | We introduce a generalization of the celebrated Lovász theta number of a
graph to simplicial complexes of arbitrary dimension. Our generalization takes
advantage of real simplicial cohomology theory, in particular combinatorial
Laplacians, and provides a semidefinite programming upper bound of the
independence number of a simplicial complex. We consider properties of the
graph theta number such as the relationship to Hoffman's ratio bound and to the
chromatic number and study how they extend to higher dimensions. Like in the
case of graphs, the higher dimensional theta number can be extended to a
hierarchy of semidefinite programming upper bounds reaching the independence
number. We analyze the value of the theta number and of the hierarchy for dense
random simplicial complexes.
| 1 | 0 | 1 | 0 | 0 | 0 |
Prediction Scores as a Window into Classifier Behavior | Most multi-class classifiers make their prediction for a test sample by
scoring the classes and selecting the one with the highest score. Analyzing
these prediction scores is useful to understand the classifier behavior and to
assess its reliability. We present an interactive visualization that
facilitates per-class analysis of these scores. Our system, called Classilist,
enables relating these scores to the classification correctness and to the
underlying samples and their features. We illustrate how such analysis reveals
varying behavior of different classifiers. Classilist is available for use
online, along with source code, video tutorials, and plugins for R, RapidMiner,
and KNIME at this https URL.
| 1 | 0 | 0 | 1 | 0 | 0 |
Effective perturbation theory for linear operators | We propose a new approach to the spectral theory of perturbed linear
operators , in the case of a simple isolated eigenvalue. We obtain two kind of
results: "radius bounds" which ensure perturbation theory applies for
perturbations up to an explicit size, and "regularity bounds" which control the
variations of eigendata to any order. Our method is based on the Implicit
Function Theorem and proceeds by establishing differential inequalities on two
natural quantities: the norm of the projection to the eigendirection, and the
norm of the reduced resolvent. We obtain completely explicit results without
any assumption on the underlying Banach space. In companion articles, on the
one hand we apply the regularity bounds to Markov chains, obtaining
non-asymptotic concentration and Berry-Ess{é}en inequalities with explicit
constants, and on the other hand we apply the radius bounds to transfer
operator of intermittent maps, obtaining explicit high-temperature regimes
where a spectral gap occurs.
| 0 | 0 | 1 | 0 | 0 | 0 |
I-MMSE relations in random linear estimation and a sub-extensive interpolation method | Consider random linear estimation with Gaussian measurement matrices and
noise. One can compute infinitesimal variations of the mutual information under
infinitesimal variations of the signal-to-noise ratio or of the measurement
rate. We discuss how each variation is related to the minimum mean-square error
and deduce that the two variations are directly connected through a very simple
identity. The main technical ingredient is a new interpolation method called
"sub-extensive interpolation method". We use it to provide a new proof of an
I-MMSE relation recently found by Reeves and Pfister [1] when the measurement
rate is varied. Our proof makes it clear that this relation is intimately
related to another I-MMSE relation also recently proved in [2]. One can
directly verify that the identity relating the two types of variation of mutual
information is indeed consistent with the one letter replica symmetric formula
for the mutual information, first derived by Tanaka [3] for binary signals, and
recently proved in more generality in [1,2,4,5] (by independent methods).
However our proof is independent of any knowledge of Tanaka's formula.
| 1 | 1 | 0 | 0 | 0 | 0 |
Non-convex Finite-Sum Optimization Via SCSG Methods | We develop a class of algorithms, as variants of the stochastically
controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the
smooth non-convex finite-sum optimization problem. Assuming the smoothness of
each component, the complexity of SCSG to reach a stationary point with
$\mathbb{E} \|\nabla f(x)\|^{2}\le \epsilon$ is $O\left (\min\{\epsilon^{-5/3},
\epsilon^{-1}n^{2/3}\}\right)$, which strictly outperforms the stochastic
gradient descent. Moreover, SCSG is never worse than the state-of-the-art
methods based on variance reduction and it significantly outperforms them when
the target accuracy is low. A similar acceleration is also achieved when the
functions satisfy the Polyak-Lojasiewicz condition. Empirical experiments
demonstrate that SCSG outperforms stochastic gradient methods on training
multi-layers neural networks in terms of both training and validation loss.
| 1 | 0 | 1 | 0 | 0 | 0 |
Minority carrier diffusion lengths and mobilities in low-doped n-InGaAs for focal plane array applications | The hole diffusion length in n-InGaAs is extracted for two samples of
different doping concentrations using a set of long and thin diffused junction
diodes separated by various distances on the order of the diffusion length. The
methodology is described, including the ensuing analysis which yields diffusion
lengths between 70 - 85 um at room temperature for doping concentrations in the
range of 5 - 9 x 10^15 cm-3. The analysis also provides insight into the
minority carrier mobility which is a parameter not commonly reported in the
literature. Hole mobilities on the order of 500 - 750 cm2/Vs are reported for
the aforementioned doping range, which are comparable albeit longer than the
majority hole mobility for the same doping magnitude in p-InGaAs. A radiative
recombination coefficient of (0.5-0.2)x10^-10 cm^-3s^-1 is also extracted from
the ensuing analysis for an InGaAs thickness of 2.7 um. Preliminary evidence is
also given for both heavy and light hole diffusion. The dark current of
InP/InGaAs p-i-n photodetectors with 25 and 15 um pitches are then calibrated
to device simulations and correlated to the extracted diffusion lengths and
doping concentrations. An effective Shockley-Read-Hall lifetime of between
90-200 us provides the best fit to the dark current of these structures.
| 0 | 1 | 0 | 0 | 0 | 0 |
Layered semi-convection and tides in giant planet interiors - I. Propagation of internal waves | Layered semi-convection is a possible candidate to explain Saturn's
luminosity excess and the abnormally large radius of some hot Jupiters. In
giant planet interiors, it could lead to the creation of density staircases,
which are convective layers separated by thin stably stratified interfaces. We
study the propagation of internal waves in a region of layered semi-convection,
with the aim to predict energy transport by internal waves incident upon a
density staircase. The goal is then to understand the resulting tidal
dissipation when these waves are excited by other bodies such as moons in giant
planets systems. We use a local Cartesian analytical model, taking into account
the complete Coriolis acceleration at any latitude, thus generalizing previous
works. We find transmission of incident internal waves to be strongly affected
by the presence of a density staircase, even if these waves are initially pure
inertial waves (which are restored by the Coriolis acceleration). In
particular, low-frequency waves of all wavelengths are perfectly transmitted
near the critical latitude. Otherwise, short-wavelength waves are only
efficiently transmitted if they are resonant with a free mode (interfacial
gravity wave or short-wavelength inertial mode) of the staircase. In all other
cases, waves are primarily reflected unless their wavelengths are longer than
the vertical extent of the entire staircase (not just a single step). We expect
incident internal waves to be strongly affected by the presence of a density
staircase in a frequency-, latitude- and wavelength-dependent manner. First,
this could lead to new criteria to probe the interior of giant planets by
seismology; and second, this may have important consequences for tidal
dissipation and our understanding of the evolution of giant planet systems.
| 0 | 1 | 0 | 0 | 0 | 0 |
A new Weber type integral equation related to the Weber-Titchmarsh problem | We derive solvability conditions and closed-form solution for the Weber type
integral equation, related to the familiar Weber-Orr integral transforms and
the old Weber-Titchmarsh problem (posed in Proc. Lond. Math. Soc. 22 (2)
(1924), pp.15, 16), recently solved by the author. Our method involves
properties of the inverse Mellin transform of integrable functions. The
Mellin-Parseval equality and some integrals, involving the Gauss hypergeometric
function are used.
| 0 | 0 | 1 | 0 | 0 | 0 |
Non-commutative Discretize-then-Optimize Algorithms for Elliptic PDE-Constrained Optimal Control Problems | In this paper, we analyze the convergence of several discretize-then-optimize
algorithms, based on either a second-order or a fourth-order finite difference
discretization, for solving elliptic PDE-constrained optimization or optimal
control problems. To ensure the convergence of a discretize-then-optimize
algorithm, one well-accepted criterion is to choose or redesign the
discretization scheme such that the resultant discretize-then-optimize
algorithm commutes with the corresponding optimize-then-discretize algorithm.
In other words, both types of algorithms would give rise to exactly the same
discrete optimality system. However, such an approach is not trivial. In this
work, by investigating a simple distributed elliptic optimal control problem,
we first show that enforcing such a stringent condition of commutative property
is only sufficient but not necessary for achieving the desired convergence. We
then propose to add some suitable $H_1$ semi-norm penalty/regularization terms
to recover the lost convergence due to the inconsistency caused by the loss of
commutativity. Numerical experiments are carried out to verify our theoretical
analysis and also validate the effectiveness of our proposed regularization
techniques.
| 0 | 0 | 1 | 0 | 0 | 0 |
Gate-Variants of Gated Recurrent Unit (GRU) Neural Networks | The paper evaluates three variants of the Gated Recurrent Unit (GRU) in
recurrent neural networks (RNN) by reducing parameters in the update and reset
gates. We evaluate the three variant GRU models on MNIST and IMDB datasets and
show that these GRU-RNN variant models perform as well as the original GRU RNN
model while reducing the computational expense.
| 1 | 0 | 0 | 1 | 0 | 0 |
Some results on the annihilators and attached primes of local cohomology modules | Let $(R, \frak m)$ be a local ring and $M$ a finitely generated $R$-module.
It is shown that if $M$ is relative Cohen-Macaulay with respect to an ideal
$\frak a$ of $R$, then $\text{Ann}_R(H_{\mathfrak{a}}^{\text{cd}(\mathfrak{a},
M)}(M))=\text{Ann}_RM/L=\text{Ann}_RM$ and
$\text{Ass}_R(R/\text{Ann}_RM)\subseteq \{\mathfrak{p} \in \text{Ass}_R
M|\,{\rm cd}(\mathfrak{a}, R/\mathfrak{p})=\text{cd}(\mathfrak{a}, M)\},$ where
$L$ is the largest submodule of $M$ such that ${\rm cd}(\mathfrak{a}, L)< {\rm
cd}(\mathfrak{a}, M)$. We also show that if $H^{\dim M}_{\mathfrak{a}}(M)=0$,
then $\text{Att}_R(H^{\dim M-1}_{\mathfrak{a}}(M))= \{\mathfrak{p} \in
\text{Supp} (M)|\,{\rm cd}(\mathfrak{a}, R/\mathfrak{p})=\dim M-1\},$ and so
the attached primes of $H^{\dim M-1}_{\mathfrak{a}}(M)$ depends only on
$\text{Supp} (M)$. Finally, we prove that if $M$ is an arbitrary module (not
necessarily finitely generated) over a Noetherian ring $R$ with ${\rm
cd}(\mathfrak{a}, M)={\rm cd}(\mathfrak{a}, R/\text{Ann}_RM)$, then
$\text{Att}_R(H^{{\rm cd}(\mathfrak{a},
M)}_{\mathfrak{a}}(M))\subseteq\{\mathfrak{p} \in V(\text{Ann}_RM)|\,{\rm
cd}(\mathfrak{a}, R/\mathfrak{p})={\rm cd}(\mathfrak{a}, M)\}.$
As a consequence of this it is shown that if $\dim M=\dim R$, then
$\text{Att}_R(H^{\dim M}_{\mathfrak{a}}(M))\subseteq\{\mathfrak{p} \in
\text{Ass}_R M|\,{\rm cd}(\mathfrak{a}, R/\mathfrak{p})=\dim M\}.$
| 0 | 0 | 1 | 0 | 0 | 0 |
Translation matrix elements for spherical Gauss-Laguerre basis functions | Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of
the type $L_{n-l-1}^{(l + 1/2)}(r^2) r^{l} Y_{lm}(\vartheta,\varphi)$, $|m|
\leq l < n \in \mathbb{N}$, constitute an orthonormal polynomial basis of the
space $L^{2}$ on $\mathbb{R}^{3}$ with radial Gaussian weight $\exp(-r^{2})$.
We have recently described reliable fast Fourier transforms for the SGL basis
functions. The main application of the SGL basis functions and our fast
algorithms is in solving certain three-dimensional rigid matching problems,
where the center is prioritized over the periphery. For this purpose, so-called
SGL translation matrix elements are required, which describe the spectral
behavior of the SGL basis functions under translations. In this paper, we
derive a closed-form expression of these translation matrix elements, allowing
for a direct computation of these quantities in practice.
| 0 | 0 | 1 | 0 | 0 | 0 |
A theoretical analysis of extending frequency-bin entanglement from photon-photon to atom-photon hybrid systems | Inspired by the recent developments in the research of atom-photon quantum
interface and energy-time entanglement between single photon pulses, we propose
to establish the concept of a special energy-time entanglement between a single
photon pulse and internal states of a single atom, which is analogous to the
frequency-bin entanglement between single photon pulses. We show that this type
of entanglement arises naturally in the interaction between frequency-bin
entangled single photon pulse pair and a single atom, via straightforward
atom-photon phase gate operations. We also discuss the properties of this type
of entanglement and show a preliminary example of its potential application in
quantum networking. Moreover, a quantum entanglement witness is constructed to
detect such entanglement from a reasonably large set of separable states.
| 0 | 1 | 0 | 0 | 0 | 0 |
Parallel Concatenation of Bayesian Filters: Turbo Filtering | In this manuscript a method for developing novel filtering algorithms through
the parallel concatenation of two Bayesian filters is illustrated. Our
description of this method, called turbo filtering, is based on a new graphical
model; this allows us to efficiently describe both the processing accomplished
inside each of the constituent filter and the interactions between them. This
model is exploited to develop two new filtering algorithms for conditionally
linear Gaussian systems. Numerical results for a specific dynamic system
evidence that such filters can achieve a better complexity-accuracy tradeoff
than marginalized particle filtering.
| 0 | 0 | 0 | 1 | 0 | 0 |
Shot noise in ultrathin superconducting wires | Quantum phase slips (QPS) may produce non-equilibrium voltage fluctuations in
current-biased superconducting nanowires. Making use of the Keldysh technique
and employing the phase-charge duality arguments we investigate such
fluctuations within the four-point measurement scheme and demonstrate that shot
noise of the voltage detected in such nanowires may essentially depend on the
particular measurement setup. In long wires the shot noise power decreases with
increasing frequency $\Omega$ and vanishes beyond a threshold value of $\Omega$
at $T \to 0$
| 0 | 1 | 0 | 0 | 0 | 0 |
Linearity of stability conditions | We study different concepts of stability for modules over a finite
dimensional algebra: linear stability, given by a "central charge", and
nonlinear stability given by the wall-crossing sequence of a "green path". Two
other concepts, finite Harder-Narasimhan stratification of the module category
and maximal forward hom-orthogonal sequences of Schurian modules, which are
always equivalent to each other, are shown to be equivalent to nonlinear
stability and to a maximal green sequence, defined using Fomin-Zelevinsky
quiver mutation, in the case the algebra is hereditary.
This is the first of a series of three papers whose purpose is to determine
all maximal green sequences of maximal length for quivers of affine type
$\tilde A$ and determine which are linear. The complete answer will be given in
the final paper [1].
| 0 | 0 | 1 | 0 | 0 | 0 |
Urban Data Streams and Machine Learning: A Case of Swiss Real Estate Market | In this paper, we show how using publicly available data streams and machine
learning algorithms one can develop practical data driven services with no
input from domain experts as a form of prior knowledge. We report the initial
steps toward development of a real estate portal in Switzerland. Based on
continuous web crawling of publicly available real estate advertisements and
using building data from Open Street Map, we developed a system, where we
roughly estimate the rental and sale price indexes of 1.7 million buildings
across the country. In addition to these rough estimates, we developed a web
based API for accurate automated valuation of rental prices of individual
properties and spatial sensitivity analysis of rental market. We tested several
established function approximation methods against the test data to check the
quality of the rental price estimations and based on our experiments, Random
Forest gives very reasonable results with the median absolute relative error of
6.57 percent, which is comparable with the state of the art in the industry. We
argue that while recently there have been successful cases of real estate
portals, which are based on Big Data, majority of the existing solutions are
expensive, limited to certain users and mostly with non-transparent underlying
systems. As an alternative we discuss, how using the crawled data sets and
other open data sets provided from different institutes it is easily possible
to develop data driven services for spatial and temporal sensitivity analysis
in the real estate market to be used for different stakeholders. We believe
that this kind of digital literacy can disrupt many other existing business
concepts across many domains.
| 1 | 0 | 0 | 1 | 0 | 0 |
BinPro: A Tool for Binary Source Code Provenance | Enforcing open source licenses such as the GNU General Public License (GPL),
analyzing a binary for possible vulnerabilities, and code maintenance are all
situations where it is useful to be able to determine the source code
provenance of a binary. While previous work has either focused on computing
binary-to-binary similarity or source-to-source similarity, BinPro is the first
work we are aware of to tackle the problem of source-to-binary similarity.
BinPro can match binaries with their source code even without knowing which
compiler was used to produce the binary, or what optimization level was used
with the compiler. To do this, BinPro utilizes machine learning to compute
optimal code features for determining binary-to-source similarity and a static
analysis pipeline to extract and compute similarity based on those features.
Our experiments show that on average BinPro computes a similarity of 81% for
matching binaries and source code of the same applications, and an average
similarity of 25% for binaries and source code of similar but different
applications. This shows that BinPro's similarity score is useful for
determining if a binary was derived from a particular source code.
| 1 | 0 | 0 | 0 | 0 | 0 |
The placement of the head that maximizes predictability. An information theoretic approach | The minimization of the length of syntactic dependencies is a
well-established principle of word order and the basis of a mathematical theory
of word order. Here we complete that theory from the perspective of information
theory, adding a competing word order principle: the maximization of
predictability of a target element. These two principles are in conflict: to
maximize the predictability of the head, the head should appear last, which
maximizes the costs with respect to dependency length minimization. The
implications of such a broad theoretical framework to understand the
optimality, diversity and evolution of the six possible orderings of subject,
object and verb are reviewed.
| 1 | 1 | 0 | 0 | 0 | 0 |
Nonparametric regression using deep neural networks with ReLU activation function | Consider the multivariate nonparametric regression model. It is shown that
estimators based on sparsely connected deep neural networks with ReLU
activation function and properly chosen network architecture achieve the
minimax rates of convergence (up to log n-factors) under a general composition
assumption on the regression function. The framework includes many well-studied
structural constraints such as (generalized) additive models. While there is a
lot of flexibility in the network architecture, the tuning parameter is the
sparsity of the network. Specifically, we consider large networks with number
of potential network parameters exceeding the sample size. The analysis gives
some insights why multilayer feedforward neural networks perform well in
practice. Interestingly, the depth (number of layers) of the neural network
architectures plays an important role and our theory suggests that for
nonparametric regression scaling the network depth with the logarithm of the
sample size is natural. It is also shown that under the composition assumption
wavelet estimators can only achieve suboptimal rates.
| 1 | 0 | 1 | 1 | 0 | 0 |
Unsupervised Learning of Neural Networks to Explain Neural Networks (extended abstract) | This paper presents an unsupervised method to learn a neural network, namely
an explainer, to interpret a pre-trained convolutional neural network (CNN),
i.e., the explainer uses interpretable visual concepts to explain features in
middle conv-layers of a CNN. Given feature maps of a conv-layer of the CNN, the
explainer performs like an auto-encoder, which decomposes the feature maps into
object-part features. The object-part features are learned to reconstruct CNN
features without much loss of information. We can consider the disentangled
representations of object parts a paraphrase of CNN features, which help people
understand the knowledge encoded by the CNN. More crucially, we learn the
explainer via knowledge distillation without using any annotations of object
parts or textures for supervision. In experiments, our method was widely used
to interpret features of different benchmark CNNs, and explainers significantly
boosted the feature interpretability without hurting the discrimination power
of the CNNs.
| 1 | 0 | 0 | 1 | 0 | 0 |
Measuring Cognitive Conflict in Virtual Reality with Feedback-Related Negativity | As virtual reality (VR) emerges as a mainstream platform, designers have
started to experiment new interaction techniques to enhance the user
experience. This is a challenging task because designers not only strive to
provide designs with good performance but also carefully ensure not to disrupt
users' immersive experience. There is a dire need for a new evaluation tool
that extends beyond traditional quantitative measurements to assist designers
in the design process. We propose an EEG-based experiment framework that
evaluates interaction techniques in VR by measuring intentionally elicited
cognitive conflict. Through the analysis of the feedback-related negativity
(FRN) as well as other quantitative measurements, this framework allows
designers to evaluate the effect of the variables of interest. We studied the
framework by applying it to the fundamental task of 3D object selection using
direct 3D input, i.e. tracked hand in VR. The cognitive conflict is
intentionally elicited by manipulating the selection radius of the target
object. Our first behavior experiment validated the framework in line with the
findings of conflict-induced behavior adjustments like those reported in other
classical psychology experiment paradigms. Our second EEG-based experiment
examines the effect of the appearance of virtual hands. We found that the
amplitude of FRN correlates with the level of realism of the virtual hands,
which concurs with the Uncanny Valley theory.
| 1 | 0 | 0 | 0 | 0 | 0 |
Strong deformations of DNA: Effect on the persistence length | Extreme deformations of the DNA double helix attracted a lot of attention
during the past decades. Particularly, the determination of the persistence
length of DNA with extreme local disruptions, or kinks, has become a crucial
problem in the studies of many important biological processes. In this paper we
review an approach to calculate the persistence length of the double helix by
taking into account the formation of kinks of arbitrary configuration. The
reviewed approach improves the Kratky--Porod model to determine the type and
nature of kinks that occur in the double helix, by measuring a reduction of the
persistence length of the kinkable DNA.
| 0 | 0 | 0 | 0 | 1 | 0 |
BézierGAN: Automatic Generation of Smooth Curves from Interpretable Low-Dimensional Parameters | Many real-world objects are designed by smooth curves, especially in the
domain of aerospace and ship, where aerodynamic shapes (e.g., airfoils) and
hydrodynamic shapes (e.g., hulls) are designed. To facilitate the design
process of those objects, we propose a deep learning based generative model
that can synthesize smooth curves. The model maps a low-dimensional latent
representation to a sequence of discrete points sampled from a rational
Bézier curve. We demonstrate the performance of our method in completing both
synthetic and real-world generative tasks. Results show that our method can
generate diverse and realistic curves, while preserving consistent shape
variation in the latent space, which is favorable for latent space design
optimization or design space exploration.
| 0 | 0 | 0 | 1 | 0 | 0 |
Raman scattering study of tetragonal magnetic phase in Sr$_{1-x}$Na$_x$Fe$_2$As$_2$: structural symmetry and electronic gap | We use inelastic light scattering to study Sr$_{1-x}$Na$_x$Fe$_2$As$_2$
($x\approx0.34$), which exhibits a robust tetragonal magnetic phase that
restores the four-fold rotation symmetry inside the orthorhombic magnetic
phase. With cooling, we observe splitting and recombination of an $E_g$ phonon
peak upon entering the orthorhombic and tetragonal magnetic phases,
respectively, consistent with the reentrant phase behavior. Our electronic
Raman data reveal a pronounced feature that is clearly associated with the
tetragonal magnetic phase, suggesting the opening of an electronic gap. No
phonon back-folding behavior can be detected above the noise level, which
implies that any lattice translation symmetry breaking in the tetragonal
magnetic phase must be very weak.
| 0 | 1 | 0 | 0 | 0 | 0 |
Learning Mixture of Gaussians with Streaming Data | In this paper, we study the problem of learning a mixture of Gaussians with
streaming data: given a stream of $N$ points in $d$ dimensions generated by an
unknown mixture of $k$ spherical Gaussians, the goal is to estimate the model
parameters using a single pass over the data stream. We analyze a streaming
version of the popular Lloyd's heuristic and show that the algorithm estimates
all the unknown centers of the component Gaussians accurately if they are
sufficiently separated. Assuming each pair of centers are $C\sigma$ distant
with $C=\Omega((k\log k)^{1/4}\sigma)$ and where $\sigma^2$ is the maximum
variance of any Gaussian component, we show that asymptotically the algorithm
estimates the centers optimally (up to constants); our center separation
requirement matches the best known result for spherical Gaussians
\citep{vempalawang}. For finite samples, we show that a bias term based on the
initial estimate decreases at $O(1/{\rm poly}(N))$ rate while variance
decreases at nearly optimal rate of $\sigma^2 d/N$.
Our analysis requires seeding the algorithm with a good initial estimate of
the true cluster centers for which we provide an online PCA based clustering
algorithm. Indeed, the asymptotic per-step time complexity of our algorithm is
the optimal $d\cdot k$ while space complexity of our algorithm is $O(dk\log
k)$.
In addition to the bias and variance terms which tend to $0$, the
hard-thresholding based updates of streaming Lloyd's algorithm is agnostic to
the data distribution and hence incurs an approximation error that cannot be
avoided. However, by using a streaming version of the classical
(soft-thresholding-based) EM method that exploits the Gaussian distribution
explicitly, we show that for a mixture of two Gaussians the true means can be
estimated consistently, with estimation error decreasing at nearly optimal
rate, and tending to $0$ for $N\rightarrow \infty$.
| 1 | 0 | 0 | 1 | 0 | 0 |
Dust in the reionization era: ALMA observations of a $z$=8.38 Galaxy | We report on the detailed analysis of a gravitationally-lensed Y-band
dropout, A2744_YD4, selected from deep Hubble Space Telescope imaging in the
Frontier Field cluster Abell 2744. Band 7 observations with the Atacama Large
Millimeter Array (ALMA) indicate the proximate detection of a significant 1mm
continuum flux suggesting the presence of dust for a star-forming galaxy with a
photometric redshift of $z\simeq8$. Deep X-SHOOTER spectra confirms the high
redshift identity of A2744_YD4 via the detection of Lyman $\alpha$ emission at
a redshift $z$=8.38. The association with the ALMA detection is confirmed by
the presence of [OIII] 88$\mu$m emission at the same redshift. Although both
emission features are only significant at the 4 $\sigma$ level, we argue their
joint detection and the positional coincidence with a high redshift dropout in
the HST images confirms the physical association. Analysis of the available
photometric data and the modest gravitational magnification ($\mu\simeq2$)
indicates A2744_YD4 has a stellar mass of $\sim$ 2$\times$10$^9$ M$_{\odot}$, a
star formation rate of $\sim20$ M$_{\odot}$/yr and a dust mass of
$\sim$6$\times$10$^{6}$ M$_{\odot}$. We discuss the implications of the
formation of such a dust mass only $\simeq$200 Myr after the onset of cosmic
reionisation.
| 0 | 1 | 0 | 0 | 0 | 0 |
Green-Blue Stripe Pattern for Range Sensing from a Single Image | In this paper, we present a novel method for rapid high-resolution range
sensing using green-blue stripe pattern. We use green and blue for designing
high-frequency stripe projection pattern. For accurate and reliable range
recovery, we identify the stripe patterns by our color-stripe segmentation and
unwrapping algorithms. The experimental result for a naked human face shows the
effectiveness of our method.
| 1 | 0 | 0 | 0 | 0 | 0 |
It Takes (Only) Two: Adversarial Generator-Encoder Networks | We present a new autoencoder-type architecture that is trainable in an
unsupervised mode, sustains both generation and inference, and has the quality
of conditional and unconditional samples boosted by adversarial learning.
Unlike previous hybrids of autoencoders and adversarial networks, the
adversarial game in our approach is set up directly between the encoder and the
generator, and no external mappings are trained in the process of learning. The
game objective compares the divergences of each of the real and the generated
data distributions with the prior distribution in the latent space. We show
that direct generator-vs-encoder game leads to a tight coupling of the two
components, resulting in samples and reconstructions of a comparable quality to
some recently-proposed more complex architectures.
| 1 | 0 | 0 | 1 | 0 | 0 |
Electrostatic gyrokinetic simulation of global tokamak boundary plasma and the generation of nonlinear intermittent turbulence | Boundary plasma physics plays an important role in tokamak confinement, but
is difficult to simulate in a gyrokinetic code due to the scale-inseparable
nonlocal multi-physics in magnetic separatrix and open magnetic field geometry.
Neutral particles are also an important part of the boundary plasma physics. In
the present paper, noble electrostatic gyrokinetic techniques to simulate the
flux-driven, low-beta electrostatic boundary plasma is reported. Gyrokinetic
ions and drift-kinetic electrons are utilized without scale-separation between
the neoclassical and turbulence dynamics. It is found that the nonlinear
intermittent turbulence is a natural gyrokinetic phenomenon in the boundary
plasma in the vicinity of the magnetic separatrix surface and in the scrape-off
layer.
| 0 | 1 | 0 | 0 | 0 | 0 |
The Montecinos-Balsara ADER-FV Polynomial Basis: Convergence Properties & Extension to Non-Conservative Multidimensional Systems | Hyperbolic systems of PDEs can be solved to arbitrary orders of accuracy by
using the ADER Finite Volume method. These PDE systems may be non-conservative
and non-homogeneous, and contain stiff source terms. ADER-FV requires a
spatio-temporal polynomial reconstruction of the data in each spacetime cell,
at each time step. This reconstruction is obtained as the root of a nonlinear
system, resulting from the use of a Galerkin method. It was proved in Jackson
[7] that for traditional choices of basis polynomials, the eigenvalues of
certain matrices appearing in these nonlinear systems are always 0, regardless
of the number of spatial dimensions of the PDEs or the chosen order of accuracy
of the ADER-FV method. This guarantees fast convergence to the Galerkin root
for certain classes of PDEs.
In Montecinos and Balsara [9] a new, more efficient class of basis
polynomials for the one-dimensional ADER-FV method was presented. This new
class of basis polynomials, originally presented for conservative systems, is
extended to multidimensional, non-conservative systems here, and the
corresponding property regarding the eigenvalues of the Galerkin matrices is
proved.
| 0 | 1 | 0 | 0 | 0 | 0 |
Reducibility of the Quantum Harmonic Oscillator in $d$-dimensions with Polynomial Time Dependent Perturbation | We prove a reducibility result for a quantum harmonic oscillator in arbitrary
dimensions with arbitrary frequencies perturbed by a linear operator which is a
polynomial of degree two in $x_j$, $-i \partial_j$ with coefficients which
depend quasiperiodically on time.
| 0 | 0 | 1 | 0 | 0 | 0 |
Model Order Selection Rules For Covariance Structure Classification | The adaptive classification of the interference covariance matrix structure
for radar signal processing applications is addressed in this paper. This
represents a key issue because many detection architectures are synthesized
assuming a specific covariance structure which may not necessarily coincide
with the actual one due to the joint action of the system and environment
uncertainties. The considered classification problem is cast in terms of a
multiple hypotheses test with some nested alternatives and the theory of Model
Order Selection (MOS) is exploited to devise suitable decision rules. Several
MOS techniques, such as the Akaike, Takeuchi, and Bayesian information criteria
are adopted and the corresponding merits and drawbacks are discussed. At the
analysis stage, illustrating examples for the probability of correct model
selection are presented showing the effectiveness of the proposed rules.
| 0 | 0 | 1 | 1 | 0 | 0 |
Enhancing Interpretability of Black-box Soft-margin SVM by Integrating Data-based Priors | The lack of interpretability often makes black-box models difficult to be
applied to many practical domains. For this reason, the current work, from the
black-box model input port, proposes to incorporate data-based prior
information into the black-box soft-margin SVM model to enhance its
interpretability. The concept and incorporation mechanism of data-based prior
information are successively developed, based on which the interpretable or
partly interpretable SVM optimization model is designed and then solved through
handily rewriting the optimization problem as a nonlinear quadratic programming
problem. An algorithm for mining data-based linear prior information from data
set is also proposed, which generates a linear expression with respect to two
appropriate inputs identified from all inputs of system. At last, the proposed
interpretability enhancement strategy is applied to eight benchmark examples
for effectiveness exhibition.
| 1 | 0 | 0 | 1 | 0 | 0 |
CollaGAN : Collaborative GAN for Missing Image Data Imputation | In many applications requiring multiple inputs to obtain a desired output, if
any of the input data is missing, it often introduces large amounts of bias.
Although many techniques have been developed for imputing missing data, the
image imputation is still difficult due to complicated nature of natural
images. To address this problem, here we proposed a novel framework for missing
image data imputation, called Collaborative Generative Adversarial Network
(CollaGAN). CollaGAN converts an image imputation problem to a multi-domain
images-to-image translation task so that a single generator and discriminator
network can successfully estimate the missing data using the remaining clean
data set. We demonstrate that CollaGAN produces the images with a higher visual
quality compared to the existing competing approaches in various image
imputation tasks.
| 1 | 0 | 0 | 1 | 0 | 0 |
A Kuroda-style j-translation | In topos theory it is well-known that any nucleus j gives rise to a
translation of intuitionistic logic into itself in a way which generalises the
Goedel-Gentzen negative translation. Here we show that there exists a similar
j-translation which is more in the spirit of Kuroda's negative translation. The
key is to apply the nucleus not only to the entire formula and universally
quantified subformulas, but to conclusions of implications as well. The
development is entirely syntactic and no knowledge of topos theory is required
to read this small note.
| 0 | 0 | 1 | 0 | 0 | 0 |
Electrical 2π phase control of infrared light in a 350nm footprint using graphene plasmons | Modulating the amplitude and phase of light is at the heart of many
applications such as wavefront shaping, transformation optics, phased arrays,
modulators and sensors. Performing this task with high efficiency and small
footprint is a formidable challenge. Metasurfaces and plasmonics are promising
, but metals exhibit weak electro-optic effects. Two-dimensional materials,
such as graphene, have shown great performance as modulators with small drive
voltages. Here we show a graphene plasmonic phase modulator which is capable of
tuning the phase between 0 and 2{\pi} in situ. With a footprint of 350nm it is
more than 30 times smaller than the 10.6$\mu$m free space wavelength. The
modulation is achieved by spatially controlling the plasmon phase velocity in a
device where the spatial carrier density profile is tunable. We provide a
scattering theory for plasmons propagating through spatial density profiles.
This work constitutes a first step towards two-dimensional transformation
optics for ultra-compact modulators and biosensing.
| 0 | 1 | 0 | 0 | 0 | 0 |
Existence of closed geodesics through a regular point on translation surfaces | We show that on any translation surface, if a regular point is contained in a
simple closed geodesic, then it is contained in infinitely many simple closed
geodesics, whose directions are dense in the unit circle. Moreover, the set of
points that are not contained in any simple closed geodesic is finite. We also
construct explicit examples showing that such points exist. For a surface in
any hyperelliptic component, we show that this finite exceptional set is
actually empty. The proofs of our results use Apisa's classifications of
periodic points and of $\GL(2,\R)$ orbit closures in hyperelliptic components,
as well as a recent result of Eskin-Filip-Wright.
| 0 | 0 | 1 | 0 | 0 | 0 |
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