cssi/SciSciGPT-SciSciNet huggingface dataset:
Comparison of NMR and crystal structures of membrane proteins and computational refinement to improve model quality.

Membrane proteins are challenging to study and restraints for structure determination are typically sparse or of low resolution because the membrane environment that surrounds them leads to a variety of experimental challenges. When membrane protein structures are determined by different techniques in different environments, a natural question is "which structure is most biologically relevant?" Towards answering this question, we compiled a dataset of membrane proteins with known structures determined by both solution NMR and X-ray crystallography. By investigating differences between the structures, we found that RMSDs between crystal and NMR structures are below 5 A in the membrane region, NMR ensembles have a higher convergence in the membrane region, crystal structures typically have a straighter transmembrane region, have higher stereo-chemical correctness, and are more tightly packed. After quantifying these differences, we used high-resolution refinement of the NMR structures to mitigate them, which paves the way for identifying and improving the structural quality of membrane proteins.
PHOTOOXIDATION OF 1-ALKENES IN ZEOLITES : A STUDY OF THE FACTORS THAT INFLUENCE PRODUCT SELECTIVITY AND FORMATION

Photochemical oxidation of hydrocarbons with molecular oxygen is potentially an environmentally benign method for the selective oxidation of hydrocarbons. In this study, in situ FT-IR spectroscopy ...
Synthesis of (−)-Noviose from 2,3-O-Isopropylidene-d-erythronolactol

Noviose is a key synthon for the construction of novobiocin, a clinically useful antitumor agent that has been shown to inhibit both type II topoisomerases and Hsp90. The synthesis of d-noviose from 2,3-O-isopropylidene-d-erythronolactol is described.
Globalization, Tax Competition and the Future of Tax Systems

This paper discusses the implications for tax systems of globalization of capital markets and of economies. It shows the extent to which particular taxes are affected by the globalization process. It speculates on future developments in this area and on tax competition.
Stiffness as a control factor for object manipulation.

The arm can behave like a spring, and this mechanical behavior can be advantageous in situations requiring rapid changes in force and/or displacement. Selection of a proper “virtual” spring before ...
Data-Driven Sparse System Identification

In this paper, we study the system identification porblem for sparse linear time-invariant systems. We propose a sparsity promoting Lasso-type estimator to identify the dynamics of the system with only a limited number of input-state data samples. Using contemporary results on high-dimensional statistics, we prove that $\Omega(k_{\max}\log(m+n))$ data samples are enough to reliably estimate the system dynamics, where n and m are the number of states and inputs, respectively, and $k_{\max}$ is the maximum number of nonzero elements in the rows of input and state matrices. The number of samples in the developed estimator is significantly smaller than the dimension of the problem for sparse systems, and yet it offers a small estimation error entry-wise. Furthermore, we show that, unlike the recently celebrated least-squares estimators for system identification problems, the method developed in this work is capable of exact recovery of the underlying sparsity structure of the system with the aforementioned number of data samples. Extensive case studies on synthetically generated systems and physical mass-spring networks are offered to demonstrate the effectiveness of the proposed method.
A New Reconfigurable Antenna MIMO Architecture for mmWave Communication

The large spectrum available in the millimeter- Wave (mmWave) band has emerged as a promising solution for meeting the huge capacity requirements of the 5th generation (5G) wireless networks. However, to fully harness the potential of mmWave communications, obstacles such as severe path loss, channel sparsity and hardware complexity should be overcome. In this paper, we introduce a generalized reconfigurable antenna multiple-input multiple-output (MIMO) architecture that takes advantage of lens-based reconfigurable antennas. The considered antennas can support multiple radiation patterns simultaneously by using a single RF chain. The degrees of freedom provided by the reconfigurable antennas are used to, first, combat channel sparsity in MIMO mmWave systems. Further, to suppress high path loss and shadowing at mmWave frequencies, we use a rate- one space-time block code. Our analysis and simulations show that the proposed reconfigurable MIMO architecture achieves full-diversity gain by using linear receivers and without requiring channel state information at the transmitter. Moreover, simulations show that the proposed architecture outperforms traditional MIMO transmission schemes in mmWave channel settings.
Characterizations of quadratic, cubic, and quartic residue matrices

Abstract We construct a collection of matrices defined by quadratic residue symbols, termed “quadratic residue matrices”, associated to the splitting behavior of prime ideals in a composite of quadratic extensions of Q , and prove a simple criterion characterizing such matrices. We also study the analogous classes of matrices constructed from the cubic and quartic residue symbols for a set of prime ideals of Q ( − 3 ) and Q ( i ) , respectively.
Exponential map and normal form for cornered asymptotically hyperbolic metrics

This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary -- cornered asymptotically hyperbolic manifolds -- and proves a theorem of Cartan-Hadamard type near infinity for the normal exponential map on the finite boundary. As a main application, a normal form for such manifolds at the corner is then constructed, analogous to the normal form for usual asymptotically hyperbolic manifolds and suited to studying geometry at the corner. The normal form is at the same time a submanifold normal form near the finite boundary and an asymptotically hyperbolic normal form near the infinite boundary.
Making Change in 2048

The 2048 game involves tiles labeled with powers of two that can be merged to form bigger powers of two; variants of the same puzzle involve similar merges of other tile values. We analyze the maximum score achievable in these games by proving a min-max theorem equating this maximum score (in an abstract generalized variation of 2048 that allows all the moves of the original game) with the minimum value that causes a greedy change-making algorithm to use a given number of coins. A widely-followed strategy in 2048 maintains tiles that represent the move number in binary notation, and a similar strategy in the Fibonacci number variant of the game (987) maintains the Zeckendorf representation of the move number as a sum of the fewest possible Fibonacci numbers; our analysis shows that the ability to follow these strategies is intimately connected with the fact that greedy change-making is optimal for binary and Fibonacci coinage. For variants of 2048 using tile values for which greedy change-making is suboptimal, it is the greedy strategy, not the optimal representation as sums of tile values, that controls the length of the game. In particular, the game will always terminate whenever the sequence of allowable tile values has arbitrarily large gaps between consecutive values.
Hodge realizations of 1-motives and the derived Albanese

We prove that the embedding of the derived category of 1-motives up to isogeny into the triangulated category of effective Voevodsky motives, as well as its left adjoint functor LAlbℚ, commute with the Hodge realization. This result yields a new proof of the rational form of Deligne's conjecture on 1-motives.
Distance-based Species Tree Estimation: Information-Theoretic Trade-off between Number of Loci and Sequence Length under the Coalescent

We consider the reconstruction of a phylogeny from multiple genes under the multispecies coalescent. We establish a connection with the sparse signal detection problem, where one seeks to distinguish between a distribution and a mixture of the distribution and a sparse signal. Using this connection, we derive an information-theoretic trade-off between the number of genes needed for an accurate reconstruction and the sequence length of the genes.
Extensions of Valuations to the Henselization and Completion

We show that if R is a local domain which is dominated by a valuation $\nu $ , then there does not always exist a regular local ring $R^{\prime }$ which birationally dominates R and is dominated by v and an extension of $\nu $ to the Henselization $(R^{\prime })^{h}$ of $R^{\prime }$ such that the associated graded rings of $R^{\prime }$ and $(R^{\prime })^{h}$ along the valuations are equal. We also show that there does not always exist $R^{\prime }$ , a prime ideal p of the completion of $\widehat R^{\prime }$ such that $p^{}\cap R^{\prime }=(0)$ and an extension of $\nu $ to $\widehat R^{\prime }$ such that the associated graded rings of $R^{\prime }$ and $R^{\prime }/p$ along the valuation are equal.
Stochastic Collocation With Non-Gaussian Correlated Process Variations: Theory, Algorithms, and Applications

Stochastic spectral methods have achieved a great success in the uncertainty quantification of many engineering problems, including variation-aware electronic and photonic design automation. State-of-the-art techniques employ generalized polynomial-chaos expansions and assume that all random parameters are independent or Gaussian correlated. This assumption is rarely true in real applications. How to handle non-Gaussian correlated random parameters is a long-standing and fundamental challenge: It is not clear how to choose basis functions and to perform a projection step in a correlated uncertain parameter space. This paper first presents a new set of basis functions to well capture the impact of non-Gaussian correlated parameters and then proposes an automatic and optimization-based quadrature method to perform projection-based stochastic collocation with a few simulation samples in the correlated parameter space. We further provide some theoretical proofs for the complexity and error bound of our proposed method. The numerical experiments on several synthetic, electronic, and photonic integrated circuit examples show the nearly exponential convergence rate of our approach and its significant ( $700 \times $ – $6000 \times $ ) speedup than Monte Carlo. Many other open problems with non-Gaussian correlated uncertainties can be further solved based on this paper.
Crepe: A Convolutional Representation for Pitch Estimation

The task of estimating the fundamental frequency of a monophonic sound recording, also known as pitch tracking, is fundamental to audio processing with multiple applications in speech processing and music information retrieval. To date, the best performing techniques, such as the pYIN algorithm, are based on a combination of DSP pipelines and heuristics. While such techniques perform very well on average, there remain many cases in which they fail to correctly estimate the pitch. In this paper, we propose a data-driven pitch tracking algorithm, CREPE, which is based on a deep convolutional neural network that operates directly on the time-domain waveform. We show that the proposed model produces state-of-the-art results, performing equally or better than pYIN. Furthermore, we evaluate the model's generalizability in terms of noise robustness. A pre-trained version of CREPE is made freely available as an open-source Python module for easy application.
Capacity Analysis of Discrete Energy Harvesting Channels

We study the channel capacity of a general discrete energy harvesting channel with a finite battery. Contrary to traditional communication systems, the transmitter of such a channel is powered by a device that harvests energy from a random exogenous energy source and has a finite-sized battery. As a consequence, at each transmission opportunity, the system can only transmit a symbol whose energy is no more than the energy currently available. This new type of power supply introduces an unprecedented input constraint for the channel, which is simultaneously random, instantaneous, and influenced by the full history of the inputs and the energy harvesting process. Furthermore, naturally, in such a channel, the energy information is observed causally at the transmitter. Both of these characteristics pose great challenges for the analysis of the channel capacity. In this paper, we use techniques developed for channels with side information and finite-state channels, to obtain lower and upper bounds on the capacity of energy harvesting channels. In particular, in a general case with Markov energy harvesting processes, we use stationarity and ergodicity theory to compute and optimize the achievable rates for the channels, and derive a series of computable capacity upper and lower bounds.
Learning Transformations for Classification Forests

Abstract: This work introduces a transformation-based learner model for classification forests. The weak learner at each split node plays a crucial role in a classification tree. We propose to optimize the splitting objective by learning a linear transformation on subspaces using nuclear norm as the optimization criteria. The learned linear transformation restores a low-rank structure for data from the same class, and, at the same time, maximizes the separation between different classes, thereby improving the performance of the split function. Theoretical and experimental results support the proposed framework.
Single-Peaked Consistency for Weak Orders Is Easy.

In economics and social choice single-peakedness is one of the most important and commonly studied models for preferences. It is well known that single-peaked consistency for total orders is in P. However in practice a preference profile is not always comprised of total orders. Often voters have indifference between some of the candidates. In a weak preference order indifference must be transitive. We show that single-peaked consistency for weak orders is in P for three different variants of single-peakedness for weak orders. Specifically, we consider Black's original definition of single-peakedness for weak orders, Black's definition of single-plateaued preferences, and the existential model recently introduced by Lackner. We accomplish our results by transforming each of these single-peaked consistency problems to the problem of determining if a 0-1 matrix has the consecutive ones property.
Expected dimensions of higher-rank Brill-Noether loci

In this paper, we prove a new expected dimension formula for certain rank two Brill-Noether loci with fixed special determinant. This answers a question asked by Osserman and also leads to a new and much simpler proof of a theorem of Osserman. Our result generalizes the well-known result by Bertram, Feinberg and independently Mukai on expected dimension of rank two Brill-Noether loci with canonical determinant and partially verifies a conjecture (in rank two) of Grzegorczyk and Newstead on coherent systems.
Temporal topic analysis with endogenous and exogenous processes

We consider the problem of modeling temporal textual data taking endogenous and exogenous processes into account. Such text documents arise in real world applications, including job advertisements and economic news articles, which are influenced by the fluctuations of the general economy. We propose a hierarchical Bayesian topic model which imposes a "group-correlated" hierarchical structure on the evolution of topics over time incorporating both processes, and show that this model can be estimated from Markov chain Monte Carlo sampling methods. We further demonstrate that this model captures the intrinsic relationships between the topic distribution and the time-dependent factors, and compare its performance with latent Dirichlet allocation (LDA) and two other related models. The model is applied to two collections of documents to illustrate its empirical performance: online job advertisements from DirectEmployers Association and journalists' postings on BusinessInsider.com.
Combinatorial Geometry of Graph Partitioning - I

The c-Balanced Separator problem is a graph-partitioning problem in which given a graph G, one aims to find a cut of minimum size such that both the sides of the cut have at least cn vertices. In this paper, we present new directions of progress in the c-Balanced Separator problem. More specifically, we propose a family of mathematical programs, that depend upon a parameter p > 0, and is an extension of the uniform version of the SDPs proposed by Goemans and Linial for this problem. In fact for the case, when p = 1, if one can solve this program in polynomial time then simply using the Goemans-Williamson’s randomized rounding algorithm for Max Cut [11] will give an O(1)-factor approximation algorithm for c-Balanced Separator improving the best known approximation factor of O( √ logn) due to Arora, Rao and Vazirani [4]. This family of programs is not convex but one can transform them into so called concave programs in which one optimizes a concave function over a convex feasible set. It is well known that the optima of such programs lie at one of the extreme points of the feasible set [26]. Our main contribution is a combinatorial characterization of some extreme points of the feasible set of the mathematical program, for p = 1 case, which to the best of our knowledge is the first of its kind. We further demonstrate how this characterization can be used to solve the program in a restricted setting. Non-convex programs have recently been investigated by Bhaskara and Vijayaraghvan [6] in which they design algorithms for approximating Matrix pnorms although their algorithmic techniques are analytical in nature. It is important to note that the properties of concave programs allows one to apply techniques due to Hoffman [18] or Tuy et al [26] to solve such problems with arbitrary accuracy that, for special forms of concave programs, converge in polynomial time. A significant portion of this work was done when the author was a B-Tech, M-Tech dual degree student at IIT-Kanpur, India ISSN 1433-8092 Electronic Colloquium on Computational Complexity, Report No. 184 (2010)
Connecting every bit of knowledge: The Structure of Wikipedia’s first link network

Abstract Apples, porcupines, and the most obscure Bob Dylan song—is every topic a few clicks from Philosophy? Within Wikipedia, the surprising answer is yes: nearly all paths lead to Philosophy. Wikipedia is the largest, most meticulously indexed collection of human knowledge ever amassed. More than information about a topic, Wikipedia is a web of naturally emerging relationships. By following the first link in each article, we algorithmically construct a directed network of all 4.7 million articles: Wikipedia's First Link Network. Here, we study the English edition of Wikipedia's First Link Network for insight into how the many articles on inventions, places, people, objects, and events are related and organized. By traversing every path, we measure the accumulation of first links, path lengths, groups of path-connected articles, and cycles. We also develop a new method, traversal funnels, to measure the influence each article exerts in shaping the network. Traversal funnels provide a new measure of influence for directed networks without spill-over into cycles, in contrast to traditional network centrality measures. Within Wikipedia's First Link Network, we find scale-free distributions describe path length, accumulation, and influence. Far from dispersed, first links disproportionately accumulate at a few articles—flowing from specific to general and culminating around fundamental notions such as Community, State, and Science. Philosophy directs more paths than any other article by two orders of magnitude. We also observe a gravitation toward topical articles such as Health Care and Fossil Fuel. These findings enrich our view of the connections and structure of Wikipedia's ever growing store of knowledge.
Sequence-structure relations of biopolymers.

Motivation DNA data is transcribed into single-stranded RNA, which folds into specific molecular structures. In this paper we pose the question to what extent sequence- and structure-information correlate. We view this correlation as structural semantics of sequence data that allows for a different interpretation than conventional sequence alignment. Structural semantics could enable us to identify more general embedded ‘patterns’ in DNA and RNA sequences. Results We compute the partition function of sequences with respect to a fixed structure and connect this computation to the mutual information of a sequence–structure pair for RNA secondary structures. We present a Boltzmann sampler and obtain the a priori probability of specific sequence patterns. We present a detailed analysis for the three PDB-structures, 2JXV (hairpin), 2N3R (3-branch multi-loop) and 1EHZ (tRNA). We localize specific sequence patterns, contrast the energy spectrum of the Boltzmann sampled sequences versus those sequences that refold into the same structure and derive a criterion to identify native structures. We illustrate that there are multiple sequences in the partition function of a fixed structure, each having nearly the same mutual information, that are nevertheless poorly aligned. This indicates the possibility of the existence of relevant patterns embedded in the sequences that are not discoverable using alignments. Availability and implementation The source code is freely available at http://staff.vbi.vt.edu/fenixh/Sampler.zip Contact duckcr@vbi.vt.edu Supplimentary information Supplementary data are available at Bioinformatics online.
Optimal orientation in branched cytoskeletal networks

Actin cytoskeletal protrusions in crawling cells, or lamellipodia, exhibit various morphological properties such as two characteristic peaks in the distribution of filament orientation with respect to the leading edge. To understand these properties, using the dendritic nucleation model as a basis for cytoskeletal restructuring, a kinetic-population model with orientational-dependent branching (birth) and capping (death) is constructed and analyzed. Optimizing for growth yields a relation between the branch angle and filament orientation that explains the two characteristic peaks. The model also exhibits a subdominant population that allows for more accurate modeling of recent measurements of filamentous actin density along the leading edge of lamellipodia in keratocytes. Finally, we explore the relationship between orientational and spatial organization of filamentous actin in lamellipodia and address recent observations of a prevalence of overlapping filaments to branched filaments-a finding that is claimed to be in contradiction with the dendritic nucleation model.
Coherent Multiple-Antenna Block-Fading Channels at Finite Blocklength

In this paper, we consider a channel model that is often used to describe mobile wireless scenarios: multiple-antenna additive white Gaussian noise channels subject to random (fading) gains with full channel state information at the receiver. The dynamics of the fading process are approximated by a piecewise-constant process (frequency non-selective isotropic block fading). This paper addresses the finite blocklength fundamental limits of this channel model. Specifically, we give a formula for the channel dispersion—a quantity governing the delay required to achieve capacity. The multiplicative nature of the fading disturbance leads to a number of interesting technical difficulties that required us to enhance traditional methods for finding the channel dispersion. Alas, one difficulty remains: the converse (impossibility) part of our result holds under an extra constraint on the growth of the peak-power with blocklength. Our results demonstrate, for example, that while the capacities of $n_{t}\times n_{r}$ and $n_{r} \times n_{t}$ antenna configurations coincide (under fixed received power), the coding delay can be sensitive to this switch. For example, at the received SNR of 20 dB, the $16\times 100$ system achieves capacity with codes of length (delay) which is only 60% of the length required for the $100\times 16$ system. Another interesting implication is that for the MISO channel, the dispersion-optimal coding schemes require employing orthogonal designs such as Alamouti’s scheme—a surprising observation considering the fact that Alamouti’s scheme was designed for reducing demodulation errors, not improving coding rate. Finding these dispersion-optimal coding schemes naturally gives a criteria for producing orthogonal design-like inputs in dimensions where orthogonal designs do not exist.
End-symmetric continued fractions and quadratic congruences

We show that for a fixed integer n 6= ±2, the congruence x +nx±1 ≡ 0 (mod α) has the solution β with 0 1 in lowest terms has a symmetric continued fraction precisely when β ≡ ±1 (mod α).
Coxeter-biCatalan combinatorics

We pose counting problems related to the various settings for Coxeter-Catalan combinatorics (noncrossing, nonnesting, clusters, Cambrian). Each problem is to count “twin” pairs of objects from a corresponding problem in Coxeter-Catalan combinatorics. We show that the problems all have the same answer, and, for a given finite Coxeter group W, we call the common solution to these problems the W-biCatalan number. We compute the W-biCatalan number for all W and take the first steps in the study of Coxeter-biCatalan combinatorics.
Oriented gain graphs, line graphs and eigenvalues

Abstract A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of gain graphs with complex units, matrix properties are established. As with graphs and signed graphs, there is a relationship between the incidence matrix of a complex unit gain graph and the adjacency matrix of the line graph.
Multimodal Generative Models for Scalable Weakly-Supervised Learning

Multiple modalities often co-occur when describing natural phenomena. Learning a joint representation of these modalities should yield deeper and more useful representations.Previous generative approaches to multi-modal input either do not learn a joint distribution or require additional computation to handle missing data. Here, we introduce a multimodal variational autoencoder (MVAE) that uses a product-of-experts inference network and a sub-sampled training paradigm to solve the multi-modal inference problem. Notably, our model shares parameters to efficiently learn under any combination of missing modalities. We apply the MVAE on four datasets and match state-of-the-art performance using many fewer parameters. In addition, we show that the MVAE is directly applicable to weakly-supervised learning, and is robust to incomplete supervision. We then consider two case studies, one of learning image transformations---edge detection, colorization, segmentation---as a set of modalities, followed by one of machine translation between two languages. We find appealing results across this range of tasks.
A non-backtracking Pólya’s theorem

P\'olya's random walk theorem states that a random walk on a $d$-dimensional grid is recurrent for $d=1,2$ and transient for $d\ge3$. We prove a version of P\'olya's random walk theorem for non-backtracking random walks. Namely, we prove that a non-backtracking random walk on a $d$-dimensional grid is recurrent for $d=2$ and transient for $d=1$, $d\ge3$. Along the way, we prove several useful general facts about non-backtracking random walks on graphs. In addition, our proof includes an exact enumeration of the number of closed non-backtracking random walks on an infinite 2-dimensional grid. This enumeration suggests an interesting combinatorial link between non-backtracking random walks on grids, and trinomial coefficients.
Stepwise Square Integrable Representations: The Concept and Some Consequences

There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on parabolic subgroups of real semisimple Lie groups, and to (infinite dimensional) locally nilpotent Lie groups. Many of these consequences are still under development. In this note I’ll survey a few of these new aspects of representation theory for nilpotent Lie groups and parabolic subgroups.
Pedestrian Detection With Autoregressive Network Phases

We present an autoregressive pedestrian detection framework with cascaded phases designed to progressively improve precision. The proposed framework utilizes a novel lightweight stackable decoder-encoder module which uses convolutional re-sampling layers to improve features while maintaining efficient memory and runtime cost. Unlike previous cascaded detection systems, our proposed framework is designed within a region proposal network and thus retains greater context of nearby detections compared to independently processed RoI systems. We explicitly encourage increasing levels of precision by assigning strict labeling policies to each consecutive phase such that early phases develop features primarily focused on achieving high recall and later on accurate precision. In consequence, the final feature maps form more peaky radial gradients emulating from the centroids of unique pedestrians. Using our proposed autoregressive framework leads to new state-of-the-art performance on the reasonable and occlusion settings of the Caltech pedestrian dataset, and achieves competitive state-of-the-art performance on the KITTI dataset.
Dynamics near the solitary waves of the supercritical gKDV equations

Abstract This work is devoted to study the dynamics of the supercritical gKDV equations near solitary waves in the energy space H 1 . We construct smooth local center-stable, center-unstable and center manifolds near the manifold of solitary waves and give a detailed description of the local dynamics near solitary waves. In particular, the instability is characterized as follows: any forward flow not starting from the center-stable manifold will leave a neighborhood of the manifold of solitary waves exponentially fast. Moreover, orbital stability is proved on the center manifold, which implies the uniqueness of the center manifold and the solutions on it exist globally and asymptotically approach the solitary waves.
Photo Wake-Up: 3D Character Animation From a Single Photo

We present a method and application for animating a human subject from a single photo. E.g., the character can walk out, run, sit, or jump in 3D. The key contributions of this paper are: 1) an application of viewing and animating humans in single photos in 3D, 2) a novel 2D warping method to deform a posable template body model to fit the person's complex silhouette to create an animatable mesh, and 3) a method for handling partial self occlusions. We compare to state-of-the-art related methods and evaluate results with human studies. Further, we present an interactive interface that allows re-posing the person in 3D, and an augmented reality setup where the animated 3D person can emerge from the photo into the real world. We demonstrate the method on photos, posters, and art. The project page is at https://grail.cs.washington.edu/projects/wakeup/.
3-D phononic crystals with ultra-wide band gaps

In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure evaluations is accomplished by a combination of a fast mixed variational eigenvalue solver and distributed Graphic Processing Unit (GPU) parallel computations. The TO algorithm utilizes the material distribution-based approach and a gradient-based optimizer. The design sensitivity for the mixed variational eigenvalue problem is derived using the adjoint method and is implemented through highly efficient vectorization techniques. We present optimized results for two-material simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC) crystal structures and show that in each of these cases different initial designs converge to single inclusion network topologies within their corresponding primitive cells. The optimized results show that large phononic stop bands for bulk wave propagation can be achieved at lower than close packed spherical configurations leading to lighter unit cells. For tungsten carbide - epoxy crystals we identify all angle all mode normalized stop bands exceeding 100%, which is larger than what is possible with only spherical inclusions.
Decentralized Control of Stochastically Switched Linear System with Unreliable Communication

We consider a networked control system (NCS) consisting of two plants, a global plant and a local plant, and two controllers, a global controller and a local controller. The global (resp. local) plant follows discrete-time stochastically switched linear dynamics with a continuous global (resp. local) state and a discrete global (resp. local) mode. We assume that the state and mode of the global plant are observed by both controllers while the state and mode of the local plant are only observed by the local controller. The local controller can inform the global controller of the local plant's state and mode through an unreliable TCP-like communication channel where successful transmissions are acknowledged. The objective of the controllers is to cooperatively minimize a modes-dependent quadratic cost over a finite time horizon. Following the method developed in [1] and [2], we construct a dynamic program based on common information and a decomposition of strategies, and use it to obtain explicit optimal strategies for the controllers. In the optimal strategies, both controllers compute a common estimate of the local plant's state. The global controller's action is linear in the state of the global plant and the common estimated state, and the local controller's action is linear in the actual states of both plants and the common estimated state. Furthermore, the gain matrices for the global controller depend on the global mode and its observation about the local mode, while the gain matrices for the local controller depend on the actual modes of both plants and the global controller's observation about the local mode.
ETH hardness for densest-k-subgraph with perfect completeness

We show that, assuming the (deterministic) Exponential Time Hypothesis, distinguishing between a graph with an induced k-clique and a graph in which all k-subgraphs have density at most 1 − e, requires nΩ(log n) time. Our result essentially matches the quasi-polynomial algorithms of Feige and Seltser [FS97] and Barman [Bar15] for this problem, and is the first one to rule out an additive PTAS for Densest k-Subgraph. We further strengthen this result by showing that our lower bound continues to hold when, in the soundness case, even subgraphs smaller by a near-polynomial factor (k′ = k · 2 −Ω(log n)) are assumed to be at most (1 − e)-dense.Our reduction is inspired by recent applications of the "birthday repetition" technique [AIM14, BKW15]. Our analysis relies on information theoretical machinery and is similar in spirit to analyzing a parallel repetition of two-prover games in which the provers may choose to answer some challenges multiple times, while completely ignoring other challenges.
Coarse differentiation of quasi-isometries II: rigidity for Sol and lamplighter groups

In this paper we prove quasi-isometric rigidity results concerning lattices in Sol and lamplighter groups. The paper builds in a substantial way on our earlier paper Coarse dierentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs.
Decentralized Charging of Plug-in Electric Vehicles With Distribution Feeder Overload Control

As the number of charging Plug-in Electric Vehicles (PEVs) increase, due to the limited power capacity of the distribution feeders and the sensitivity of the mid-way distribution transformers to the excessive load, it is crucial to control the amount of power through each specific distribution feeder to avoid system overloads that may lead to breakdowns. In this technical note we develop, analyze and evaluate charging algorithms for PEVs with feeder overload constraints in the distribution grid. The algorithms we propose jointly minimize the variance of the aggregate load and prevent overloading of the distribution feeders.
Convergence Analysis of Two-layer Neural Networks with ReLU Activation

In recent years, stochastic gradient descent (SGD) based techniques has become the standard tools for training neural networks. However, formal theoretical understanding of why SGD can train neural networks in practice is largely missing. In this paper, we make progress on understanding this mystery by providing a convergence analysis for SGD on a rich subset of two-layer feedforward networks with ReLU activations. This subset is characterized by a special structure called "identity mapping". We prove that, if input follows from Gaussian distribution, with standard $O(1/\sqrt{d})$ initialization of the weights, SGD converges to the global minimum in polynomial number of steps. Unlike normal vanilla networks, the "identity mapping" makes our network asymmetric and thus the global minimum is unique. To complement our theory, we are also able to show experimentally that multi-layer networks with this mapping have better performance compared with normal vanilla networks. Our convergence theorem differs from traditional non-convex optimization techniques. We show that SGD converges to optimal in "two phases": In phase I, the gradient points to the wrong direction, however, a potential function $g$ gradually decreases. Then in phase II, SGD enters a nice one point convex region and converges. We also show that the identity mapping is necessary for convergence, as it moves the initial point to a better place for optimization. Experiment verifies our claims.
Principal subspaces of higher-level standard $\widehat{\mathfrak{sl}(n)}$-modules

Using completions of certain universal enveloping algebras, we provide a natural setting for families of defining relations for the principal subspaces of standard modules for untwisted affine Lie algebras. We also use the theory of vertex operator algebras and intertwining operators to construct exact sequences among principal subspaces of certain standard -modules, n ≥ 3. As a consequence, we obtain the multigraded dimensions of the principal subspaces W(k1Λ1 + k2Λ2) and W(kn-2Λn-2 + kn-1Λn-1). This generalizes earlier work by Calinescu on principal subspaces of standard -modules.
Optimizing data freshness, throughput, and delay in multi-server information-update systems

In this work, we investigate the design of information-update systems, where incoming update packets are forwarded to a remote destination through multiple servers (each server can be viewed as a wireless channel). One important performance metric of these systems is the data freshness at the destination, also called the age-of-information or simply age, which is defined as the time elapsed since the freshest packet at the destination was generated. Recent studies on information-update systems have shown that the age-of-information can be reduced by intelligently dropping stale packets. However, packet dropping may not be appropriate in many applications, such as news and social updates, where users are interested in not just the latest updates, but also past news. Therefore, all packets may need to be successfully delivered. In this paper, we study how to optimize age-of-information without throughput loss. We consider a general scenario where incoming update packets do not necessarily arrive in the order of their generation times. We prove that a preemptive Last Generated First Served (LGFS) policy simultaneous optimizes the age, throughput, and delay performance in infinite buffer queueing systems. We also show age-optimality for the LGFS policy for any finite queue size. These results hold for arbitrary, including non-stationary, arrival processes.
Logistics of Mathematical Modeling-Focused Projects

AbstractThis article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower- and upper-division mathematics courses with an emphasis on mathematical modeling and data collection. Projects provide tangible connections to course content, which can motivate students to learn at a deeper level. Logistical pitfalls and insights are highlighted, as well as descriptions of several key implementation resources. Effective assessment tools, which allowed a smooth adjustment to student feedback, are demonstrated for a sample class. As I smoothed the transition into each project and guided students through the use of the technology, their negative feedback on projects decreased and more students noted how the projects had enhanced their understanding of the course topics. Best practices learned over the years ar...
The metric-restricted inverse design problem

We study a class of design problems in solid mechanics, leading to a variation on the classical question of equi-dimensional embeddability of Riemannian manifolds. In this general new context, we derive a necessary and sufficient existence condition, given through a system of total differential equations, and discuss its integrability. In the classical context, the same approach yields conditions of immersibility of a given metric in terms of the Riemann curvature tensor. In the present situation, the equations do not close in a straightforward manner, and successive differentiation of the compatibility conditions leads to a new algebraic description of integrability. We also recast the problem in a variational setting and analyze the infimum of the appropriate incompatibility energy, resembling the non-Euclidean elasticity. We then derive a -convergence result for dimension reduction from 3d to 2d in the Kirchhoff energy scaling regime.
$C^m$ Eigenfunctions of Perron–Frobenius operators and a new approach to numerical computation of Hausdorff dimension: applications in $\mathbb R^1$

We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case that we consider here, our methods require only $C^3$ regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linear, Perron-Frobenius operators $L_s$. The operators $L_s$ can typically be studied in many different Banach spaces. Here, unlike most of the literature, we study $L_s$ in a Banach space of real-valued, $C^k$ functions, $k \ge 2$. We note that $L_s$ is not compact, but has essential spectral radius $\rho_s$ strictly less than the spectral radius $\lambda_s$ and possesses a strictly positive $C^k$ eigenfunction $v_s$ with eigenvalue $\lambda_s$. Under appropriate assumptions on the IFS, the Hausdorff dimension of the invariant set of the IFS is the value $s=s_*$ for which $\lambda_s =1$. This eigenvalue problem is then approximated by a collocation method using continuous piecewise linear functions. Using the theory of positive linear operators and explicit a priori bounds on the derivatives of the strictly positive eigenfunction $v_s$, we give rigorous upper and lower bounds for the Hausdorff dimension $s_*$, and these bounds converge to $s_*$ as the mesh size approaches zero.
Bridging the capacity gap between interactive and one-way communication

We study the communication rate of coding schemes for interactive communication that transform any two-party interactive protocol into a protocol that is robust to noise.Recently, Haeupler [11] showed that if an ϵ > 0 fraction of transmissions are corrupted, adversarially or randomly, then it is possible to achieve a communication rate of [EQUATION]. Furthermore, Haeupler conjectured that this rate is optimal for general input protocols. This stands in contrast to the classical setting of one-way communication in which error-correcting codes are known to achieve an optimal communication rate of 1 − Θ (H(ϵ)) = 1 − O (ϵ).In this work, we show that the quadratically smaller rate loss of the one-way setting can also be achieved in interactive coding schemes for a very natural class of input protocols. We introduce the notion of average message length, or the average number of bits a party sends before receiving a reply, as a natural parameter for measuring the level of interactivity in a protocol. Moreover, we show that any protocol with average message length e = Ω(poly(1/ϵ)) can be simulated by a protocol with optimal communication rate 1 − Θ(H(ϵ)) over an oblivious adversarial channel with error fraction ϵ. Furthermore, under the additional assumption of access to public shared randomness, the optimal communication rate is achieved ratelessly, i.e., the communication rate adapts automatically to the actual error rate ϵ without having to specify it in advance.This shows that the capacity gap between one-way and interactive communication can be bridged even for very small (constant in ϵ) average message lengths, which are likely to be found in many applications.
Optical Kerr Effect in Organic Ultrastrongly Coupled Cavity Polaritons: Theory and Experiment

We summarize the materials, experiments, the most revealing findings and describe the extensions of previous theory approaches to NLO processes in polaritonic matter as they relate to recent experiments in organic ultrastrongly coupled cavity polaritons.
One-dimensional model equations for hyperbolic fluid flow

Abstract In this paper we study the singularity formation for two nonlocal 1D active scalar equations, focusing on the hyperbolic flow scenario. Those 1D equations can be regarded as simplified models of some 2D fluid equations.
Higher regularity of the free boundary in the obstacle problem for the fractional Laplacian

Abstract We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack estimate.
Right for the Right Reasons: Training Differentiable Models by Constraining their Explanations.

Neural networks are among the most accurate supervised learning methods in use today, but their opacity makes them difficult to trust in critical applications, especially when conditions in training differ from those in test. Recent work on explanations for black-box models has produced tools (e.g. LIME) to show the implicit rules behind predictions, which can help us identify when models are right for the wrong reasons. However, these methods do not scale to explaining entire datasets and cannot correct the problems they reveal. We introduce a method for efficiently explaining and regularizing differentiable models by examining and selectively penalizing their input gradients, which provide a normal to the decision boundary. We apply these penalties both based on expert annotation and in an unsupervised fashion that encourages diverse models with qualitatively different decision boundaries for the same classification problem. On multiple datasets, we show our approach generates faithful explanations and models that generalize much better when conditions differ between training and test.