cssi/SciSciGPT-SciSciNet huggingface dataset:
Pooled library screening with multiplexed Cpf1 library.

Capitalizing on the inherent multiplexing capability of AsCpf1, we developed a multiplexed, high-throughput screening strategy that minimizes library size without sacrificing gene targeting efficiency. We demonstrated that AsCpf1 can be used for functional genomics screenings and that an AsCpf1-based multiplexed library performs similarly as compared to currently available monocistronic CRISPR/Cas9 libraries, with only one vector required for each gene. We construct the smallest whole-genome CRISPR knock-out library, Mini-human, for the human genome (n = 17,032 constructs targeting 16,977 protein-coding genes), which performs favorably compared to conventional Cas9 libraries. AsCpf1 is an alternative nuclease to Cas9 for CRISPR mediated genome engineering. Here the authors demonstrate functional genomic screens with AsCpf1 that minimize library size with no loss in gene targeting efficiency.
Neuroevolution for RTS Micro

This paper uses neuroevolution of augmenting topologies to evolve control tactics for groups of units in real-time strategy games. In such games, players build economies to generate armies composed of multiple types of units with different attack and movement characteristics to combat each other. This paper evolves neural networks to control movement and attack commands, also called micro, for a group of ranged units skirmishing with a group of melee units. Our results show that neuroevolution of augmenting topologies can effectively generate neural networks capable of good micro for our ranged units against a group of hand-coded melee units. The evolved neural networks lead to kiting behavior for the ranged units which is a common tactic used by professional players in ranged versus melee skirmishes in popular real-time strategy games like Starcraft. The evolved neural networks also generalized well to other starting positions and numbers of units. We believe these results indicate the potential of neuroevolution for generating effective micro in real-time strategy games.
Convergence analysis of proximal gradient with momentum for nonconvex optimization

In this work, we investigate the accelerated proximal gradient method for nonconvex programming (APGnc). The method compares between a usual proximal gradient step and a linear extrapolation step, and accepts the one that has a lower function value to achieve a monotonic decrease. In specific, under a general nonsmooth and nonconvex setting, we provide a rigorous argument to show that the limit points of the sequence generated by APGnc are critical points of the objective function. Then, by exploiting the Kurdyka-Łojasiewicz (KŁ) property for a broad class of functions, we establish the linear and sub-linear convergence rates of the function value sequence generated by APGnc. We further propose a stochastic variance reduced APGnc (SVRG-APGnc), and establish its linear convergence under a special case of the KŁ property. We also extend the analysis to the inexact version of these methods and develop an adaptive momentum strategy that improves the numerical performance.
Asymptotic Network Robustness

This paper examines the dependence of network performance measures on network size and considers scaling results for large networks. We connect two performance measures that are well studied, but appear to be unrelated. The first measure is concerned with energy metrics, namely, the $\mathcal {H}_2$ -norm of a network, which arises in control theory applications. The second measure is concerned with the notion of “tail risk,” which arises in economic and financial networks. We study the question of why such performance measures may deteriorate at a faster rate than the growth rate of the network. We first focus on the energy metric and its well-known connection to controllability Gramian of the underlying dynamical system. We show that undirected networks exhibit the most graceful energy growth rates as network size grows. This rate is quantified completely by the proximity of the spectral radius to unity or distance to instability. In contrast, we show that the simple characterization of energy in terms of network spectrum does not exist for directed networks. We demonstrate that for any fixed distance to instability, energy of a directed network can grow at an exponentially faster rate. We provide general methods for manipulating networks to reduce energy. In particular, we prove that certain operations that increase the symmetry in a network cannot increase energy (in an order sense). Additionally, we demonstrate that such operations can effectively reduce energy for many network topologies. Second, we focus on tail risk in economic and financial networks. In contrast to the $\mathcal {H}_2$ -norm, which arises from computing the expectation of energy in the network, tail risk focuses on tail probability behavior of network variables. Although the two measures differ substantially, we show that they are precisely connected through the system Gramian. This surprising result explains why topology considerations rather than specific performance measures dictate the large-scale behavior of networks. Finally, we demonstrate the consistency of our theory with simulations on synthetic and real-life networks.
Isotropically random orthogonal matrices: Performance of LASSO and minimum conic singular values

Recently, the precise performance of the Generalized LASSO algorithm for recovering structured signals from compressed noisy measurements, obtained via i.i.d. Gaussian matrices, has been characterized. The analysis is based on a framework introduced by Stojnic and heavily relies on the use of Gordon's Gaussian min-max theorem (GMT), a comparison principle on Gaussian processes. As a result, corresponding characterizations for other ensembles of measurement matrices have not been developed. In this work, we analyze the corresponding performance of the ensemble of isotropically random orthogonal (i.r.o.) measurements. We consider the constrained version of the Generalized LASSO and derive a sharp characterization of its normalized squared error in the large-system limit. When compared to its Gaussian counterpart, our result analytically confirms the superiority in performance of the i.r.o. ensemble. Our second result, derives an asymptotic lower bound on the minimum conic singular values of i.r.o. matrices. This bound is larger than the corresponding bound on Gaussian matrices. To prove our results we express i.r.o. matrices in terms of Gaussians and show that, with some modifications, the GMT framework is still applicable.
Multi-cores, posets, and lattice paths ☆

Abstract Hooks are prominent in representation theory (of symmetric groups) and they play a role in number theory (via cranks associated to Ramanujan's congruences). A partition of a positive integer n has a Young diagram representation. To each cell in the diagram there is an associated statistic called hook length, and if a number t is absent from the diagram then the partition is called a t-core. A partition is an ( s , t ) -core if it is both an s- and a t-core. Since the work of Anderson on ( s , t ) -cores, the topic has received growing attention. This paper expands the discussion to multiple-cores. More precisely, we explore ( s , s + 1 , … , s + k ) -core partitions much in the spirit of a recent paper by Stanley and Zanello. In fact, our results exploit connections between three combinatorial objects: multi-cores, posets and lattice paths (with a novel generalization of Dyck paths). Additional results and conjectures are scattered throughout the paper. For example, one of these statements implies a curious symmetry for twin-coprime ( s , s + 2 ) -core partitions.
Generation of Virtual Dual Energy Images from Standard Single-Shot Radiographs Using Multi-scale and Conditional Adversarial Network.

Dual-energy (DE) chest radiographs provide greater diagnostic information than standard radiographs by separating the image into bone and soft tissue, revealing suspicious lesions which may otherwise be obstructed from view. However, acquisition of DE images requires two physical scans, necessitating specialized hardware and processing, and images are prone to motion artifact. Generation of virtual DE images from standard, single-shot chest radiographs would expand the diagnostic value of standard radiographs without changing the acquisition procedure. We present a Multi-scale Conditional Adversarial Network (MCA-Net) which produces high-resolution virtual DE bone images from standard, single-shot chest radiographs. Our proposed MCA-Net is trained using the adversarial network so that it learns sharp details for the production of high-quality bone images. Then, the virtual DE soft tissue image is generated by processing the standard radiograph with the virtual bone image using a cross projection transformation. Experimental results from 210 patient DE chest radiographs demonstrated that the algorithm can produce high-quality virtual DE chest radiographs. Important structures were preserved, such as coronary calcium in bone images and lung lesions in soft tissue images. The average structure similarity index and the peak signal to noise ratio of the produced bone images in testing data were 96.4 and 41.5, which are significantly better than results from previous methods. Furthermore, our clinical evaluation results performed on the publicly available dataset indicates the clinical values of our algorithms. Thus, our algorithm can produce high-quality DE images that are potentially useful for radiologists, computer-aided diagnostics, and other diagnostic tasks.
Materials selection rules for amorphous complexion formation in binary metallic alloys

Abstract Complexions are phase-like interfacial features that can influence a wide variety of properties, but the ability to predict which material systems can sustain these features remains limited. Amorphous complexions are of particular interest due to their ability to enhance diffusion and damage tolerance mechanisms, as a result of the excess free volume present in these structures. In this paper, we propose a set of materials selection rules aimed at predicting the formation of amorphous complexions, with an emphasis on (1) encouraging the segregation of dopants to the interfaces and (2) lowering the formation energy for a glassy structure. To validate these predictions, binary Cu-rich metallic alloys encompassing a range of thermodynamic parameter values were created using sputter deposition and subsequently heat treated to allow for segregation and transformation of the boundary structure. All of the alloys studied here experienced dopant segregation to the grain boundary, but exhibited different interfacial structures. Cu-Zr and Cu-Hf formed nanoscale amorphous intergranular complexions while Cu-Nb and Cu-Mo retained crystalline order at their grain boundaries, which can mainly be attributed to differences in the enthalpy of mixing. Finally, using our newly formed materials selection rules, we extend our scope to a Ni-based alloy to further validate our hypothesis, as well as make predictions for a wide variety of transition metal alloys.
FIRST DETECTION OF c-C3H2 IN A CIRCUMSTELLAR DISK

We report the first detection of c-C{sub 3}H{sub 2} in a circumstellar disk. The c-C{sub 3}H{sub 2} J = 6-5 line (217.882 GHz) is detected and imaged through Atacama Large Millimeter Array (ALMA) Science Verification observations toward the disk around the Herbig Ae star HD 163296 at 0.''8 resolution. The emission is consistent with that arising from a Keplerian rotating disk. Two additional c-C{sub 3}H{sub 2} transitions are also tentatively detected, bolstering the identification of this species, but with insufficient signal-to-noise ratio to constrain the spatial distribution. Using a previously developed model for the physical structure of this disk, we fit a radial power-law distribution model to the c-C{sub 3}H{sub 2} 6-5 emission and find that c-C{sub 3}H{sub 2} is present in a ring structure from an inner radius of about 30 AU to an outer radius of about 165 AU. The column density is estimated to be 10{sup 12}-10{sup 13} cm{sup -2}. The clear detection and intriguing ring structure suggest that c-C{sub 3}H{sub 2} has the potential to become a useful probe of radiation penetration in disks.
On falsification of the binary instrumental variable model

Instrumental variables are widely used for estimating causal effects in the presence of unmeasured confounding. The discrete instrumental variable model has testable implications for the law of the observed data. However, current assessments of instrumental validity are typically based solely on subject-matter arguments rather than these testable implications, partly due to a lack of formal statistical tests with known properties. In this paper, we develop simple procedures for testing the binary instrumental variable model. Our methods are based on existing techniques for comparing two treatments, such as the [Formula: see text]-test and the Gail-Simon test. We illustrate the importance of testing the instrumental variable model by evaluating the exogeneity of college proximity using the National Longitudinal Survey of Young Men.
A Combinatorial Derivation of the Number of Labeled Forests

Lajos Takacs gave a somewhat formidable alternating sum expression for the num- ber of forests of unrooted trees on n labeled vertices. Here we use a weight-reversing involution on suitable tree conflgurations to give a combinatorial derivation of Takacs' result.
Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem

We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in discrete time, and consider how to remove or reduce the bias. We point out the difficulty is that the heat flow is exactly solvable, but neither its forward nor backward method is implementable in general, except for Gaussian data. We propose the symmetrized Langevin algorithm (SLA), which should have a smaller bias than ULA, at the price of implementing a proximal gradient step in space. We show SLA is in fact consistent for Gaussian target measure, whereas ULA is not. We also illustrate various algorithms explicitly for Gaussian target measure, including gradient descent, proximal gradient, and Forward-Backward, and show they are all consistent.
Design of adiabatic MTJ-CMOS hybrid circuits

Low-power designs are a necessity with the increasing demand of portable devices which are battery operated. In many of such devices the operational speed is not as important as battery life. Logic-in-memory structures using nano-devices and adiabatic designs are two methods to reduce the static and dynamic power consumption respectively. Magnetic tunnel junction (MTJ) is an emerging technology which has many advantages when used in logic-in-memory structures in conjunction with CMOS. In this paper, we introduce a novel adiabatic hybrid MTJ/CMOS structure which is used to design AND/NAND, XOR/XNOR and 1-bit full adder circuits. We simulate the designs using HSPICE with 32nm CMOS technology and compared it with a non-adiabatic hybrid MTJ/CMOS circuits. The proposed adiabatic MTJ/CMOS full adder design has more than 7 times lower power consumtion compared to the previous MTJ/CMOS full adder.
Infinitely generated semigroups and polynomial complexity

This paper continues the functional approach to the P-vs.-NP problem, begun in [J. C. Birget, Semigroups and one-way functions, Internat. J. Algebra Comput. 25 (1–2) (2015) 3–36]. Here, we focus on the monoid ℛℳ2P of right-ideal morphisms of the free monoid, that have polynomial input balance and polynomial time-complexity. We construct a machine model for the functions in ℛℳ2P, and evaluation functions. We prove that, ℛℳ2P is not finitely generated, and use this to show separation results for time-complexity.
Polarimetric Thermal to Visible Face Verification via Attribute Preserved Synthesis

Thermal to visible face verification is a challenging problem due to the large domain discrepancy between the modalities. Existing approaches either attempt to synthesize visible faces from thermal faces or extract robust features from these modalities for cross-modal matching. In this paper, we take a different approach in which we make use of the attributes extracted from the visible image to synthesize the attribute-preserved visible image from the input thermal image for cross-modal matching. A pre-trained VGG-Face network is used to extract the attributes from the visible image. Then, a novel Attribute Preserved Generative Adversarial Network (AP-GAN) is proposed to synthesize the visible image from the thermal image guided by the extracted attributes. Finally, a deep network is used to extract features from the synthesized image and the input visible image for verification. Extensive experiments on the ARL Polarimetric face dataset show that the proposed method achieves significant improvements over the state-of-the-art methods.
Variable elimination in the Fourier domain

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major computational advantages. We explore a different type of compact representation based on discrete Fourier representations, complementing the classical approach based on conditional independencies. We show that a large class of probabilistic graphical models have a compact Fourier representation. This theoretical result opens up an entirely new way of approximating a probability distribution. We demonstrate the significance of this approach by applying it to the variable elimination algorithm. Compared with the traditional bucket representation and other approximate inference algorithms, we obtain significant improvements.
SpeedRead: A Fast Named Entity Recognition Pipeline

Online content analysis employs algorithmic methods to identify entities in unstructured text. Both machine learning and knowledge-base approaches lie at the foundation of contemporary named entities extraction systems. However, the progress in deploying these approaches on web-scale has been been hampered by the computational cost of NLP over massive text corpora. We present SpeedRead (SR), a named entity recognition pipeline that runs at least 10 times faster than Stanford NLP pipeline. This pipeline consists of a high performance Penn Treebankcompliant tokenizer, close to state-of-art part-of-speech (POS) tagger and knowledge-based named entity recognizer.
Validity of the “Sharp-Kink Approximation” for Water and Other Fluids

The contact angle of a liquid droplet on a solid surface is a direct measure of fundamental atomic-scale forces acting between liquid molecules and the solid surface. In this work, the validity is assessed of a simple equation, which approximately relates the contact angle of a liquid on a surface to its density, its surface tension, and the effective molecule-surface potential. This equation is derived in the sharp-kink approximation, where the density profile of the liquid is assumed to drop precipitously within one molecular diameter of the substrate. It is found that this equation satisfactorily reproduces the temperature-dependence of the contact angle for helium on alkali metal surfaces. The equation also seems be applicable to liquids such as water on solid surfaces such as gold and graphite, on the basis of a comparison of predicted and measured contact angles near room-temperature. Nevertheless, we conclude that, to fully test the equation's applicability to fluids such as water, it remains necessary to measure the contact angle's temperature-dependence. We hypothesize that the effects of electrostatic forces can increase with temperature, potentially driving the wetting temperature much higher and closer to the critical point, or lower, closer to room temperature, than predicted using current theories.
Multi-parameter singular Radon transforms

The purpose of this announcement is to describe a development given in a series of forthcoming papers by the authors that concern operators of the form \[ f\mapsto \psi(x) \int f(\gamma_t(x)) K(t)\: dt, \] where $\gamma_t(x)=\gamma(t,x)$ is a $C^\infty$ function defined on a neighborhood of the origin in $(t,x)\in \mathbb{R}^N\times \mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $K(t)$ is a "multi-parameter singular kernel" supported near $t=0$, and $\psi$ is a cutoff function supported near $x=0$. This note concerns the case when $K$ is a "product kernel". The goal is to give conditions on $\gamma$ such that the above operator is bounded on $L^p$ for $1<p<\infty$. Associated maximal functions are also discussed. The "single-parameter" case when $K$ is a Calder\'on-Zygmund kernel was studied by Christ, Nagel, Stein, and Wainger. The theory here extends these results to the multi-parameter context and also deals effectively with the case when $\gamma$ is real-analytic.
PointConv: Deep Convolutional Networks on 3D Point Clouds

Unlike images which are represented in regular dense grids, 3D point clouds are irregular and unordered, hence applying convolution on them can be difficult. In this paper, we extend the dynamic filter to a new convolution operation, named PointConv. PointConv can be applied on point clouds to build deep convolutional networks. We treat convolution kernels as nonlinear functions of the local coordinates of 3D points comprised of weight and density functions. With respect to a given point, the weight functions are learned with multi-layer perceptron networks and the density functions through kernel density estimation. A novel reformulation is proposed for efficiently computing the weight functions, which allowed us to dramatically scale up the network and significantly improve its performance. The learned convolution kernel can be used to compute translation-invariant and permutation-invariant convolution on any point set in the 3D space. Besides, PointConv can also be used as deconvolution operators to propagate features from a subsampled point cloud back to its original resolution. Experiments on ModelNet40, ShapeNet, and ScanNet show that deep convolutional neural networks built on PointConv are able to achieve state-of-the-art on challenging semantic segmentation benchmarks on 3D point clouds. Besides, our experiments converting CIFAR-10 into a point cloud showed that networks built on PointConv can match the performance of convolutional networks in 2D images of a similar structure.
Sparse Inverse Covariance Estimation for Chordal Structures

In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems. Recently, we have shown that the sparsity pattern of the optimal solution of GL is equivalent to the one obtained from simply thresholding the sample covariance matrix, for sparse graphs under different conditions. We have also derived a closed-form solution that is optimal when the thresholded sample covariance matrix has an acyclic structure. As a major generalization of the previous result, in this paper we derive a closed-form solution for the GL for graphs with chordal structures. We show that the GL and thresholding equivalence conditions can significantly be simplified and are expected to hold for high-dimensional problems if the thresholded sample covariance matrix has a chordal structure. We then show that the GL and thresholding equivalence is enough to reduce the GL to a maximum determinant matrix completion problem and drive a recursive closed-form solution for the GL when the thresholded sample covariance matrix has a chordal structure. For large-scale problems with up to 450 million variables, the proposed method can solve the GL problem in less than 2 minutes, while the state-of-the-art methods converge in more than 2 hours.
Accurately Accounting for Random Blockage in Device-to-Device mmWave Networks

Millimeter-wave systems are characterized by the use of highly directional antennas and the presence of blockages, which significantly alter the path-loss and small-scale fading parameters. The received power of each interferer depends on the direction it points and whether it is line-of- sight (LOS), non-LOS (i.e., partially blocked), or completely blocked. While interferers that are sufficiently far away will almost certainly be completely blocked, a finite number of interferers in close proximity will be subject to random partial blockages. Previous attempts to characterize mmWave networks have made the simplifying assumption that all interferers within some radius, called the LOS ball, are unblocked, while interferers beyond that radius are non-LOS. However, compared to simulation results, the LOS ball assumption tends to overestimate outage. In this paper, we present an accurate yet tractable analysis of finite mmWave networks that dispenses with the LOS ball assumption. In the analysis, each interferer has a distribution that is selected randomly from several possibilities, each representing different blockage and directivity states. First, the exact outage probability is found for a finite network with interferers in fixed locations. Then, the spatially averaged outage probability is found by averaging over the interferer locations. While the focus is on device-to-device networks, the analysis is general enough to find applications outside of the present mmWave framework.
Symplectic Non-Squeezing for the Cubic NLS on the Line

We prove symplectic non-squeezing for the cubic nonlinear Schrodinger equation on the line via finite-dimensional approximation.
MDPs with unawareness

Markov decision processes (MDPs) are widely used for modeling decision-making problems in robotics, automated control, and economics. Traditional MDPs assume that the decision maker (DM) knows all states and actions. However, this may not be true in many situations of interest. We define a new framework, MDPs with unawareness (MDPUs) to deal with the possibilities that a DM may not be aware of all possible actions. We provide a complete characterization of when a DM can learn to play near-optimally in an MDPU, and give an algorithm that learns to play near-optimally when it is possible to do so, as efficiently as possible. In particular, we characterize when a near-optimal solution can be found in polynomial time.
Fundamental solutions for isotropic size-dependent couple stress elasticity

Abstract Fundamental solutions for two- and three-dimensional linear isotropic size-dependent couple stress elasticity are derived, based upon the decomposition of displacement fields into dilatational and solenoidal components. While several fundamental solutions have appeared previously in the literature, the present version is for the newly developed fully determinate couple stress theory. Within this theory, the couple stress tensor is skew-symmetrical and thus possesses vectorial character. The present derivation provides solutions for infinite domains of elastic materials under the influence of unit concentrated forces and couples. Unlike all previous work, unique solutions for displacements, rotations, force-stresses and couple-stresses are established, along with the corresponding force-tractions and couple-tractions. These fundamental solutions are central in analysis methods based on Green’s functions for infinite domains and are required as kernels in the corresponding boundary integral formulations for size-dependent couple stress elastic materials.
ANY FLAT BUNDLE ON A PUNCTURED DISC HAS AN OPER STRUCTURE

We prove that any flat $G$-bundle, where $G$ is a complex connected reductive algebraic group, on the punctured disc admits the structure of an oper. This result is important in the local geometric Langlands correspondence proposed in \cite{FG}. Our proof uses certain deformations of the affine Springer fibers which could be of independent interest. As a byproduct, we construct representations of affine Weyl groups on the homology of these deformations generalizing representations constructed by Lusztig.
Spectrum and Heat Kernel Asymptotics on General Laakso Spaces

We introduce a method of constructing a general Laakso space while calculating the spectrum and multiplicities of the Laplacian operator. Using this information, we find the leading term of the trace of the heat kernel and the spectral dimension on an arbitrary Laakso space.
Dynamic Question Ordering in Online Surveys

Online surveys have the potential to support adaptive questions, where later questions depend on earlier responses. Past work has taken a rule-based approach, uniformly across all respondents. We envision a richer interpretation of adaptive questions, which we call Dynamic Question Ordering (DQO), where question order is personalized. Such an approach could increase engagement, and therefore response rate, as well as imputation quality. We present a DQO framework to improve survey completion and imputation. In the general survey-taking setting, we want to maximize survey completion, and so we focus on ordering questions to engage the respondent and collect hopefully all information, or at least the information that most characterizes the respondent, for accurate imputations. In another scenario, our goal is to provide a personalized prediction. Since it is possible to give reasonable predictions with only a subset of questions, we are not concerned with motivating users to answer all questions. Instead, we want to order questions to get information that reduces prediction uncertainty, while not being too burdensome. We illustrate this framework with two case studies, for the prediction and survey-taking settings. We also discuss DQO for national surveys and consider connections between our statistics-based question-ordering approach and cognitive survey methodology
On the Cohomological Spectrum and Support Varieties for Infinitesimal Unipotent Supergroup Schemes

We show that if G is an infinitesimal elementary supergroup scheme of height \(\le r\), then the cohomological spectrum \(\left| G \right| \) of G is naturally homeomorphic to the variety \(\mathscr {N}_r(G)\) of supergroup homomorphisms \(\rho : \mathbb {M}_r\rightarrow G\) from a certain (non-algebraic) affine supergroup scheme \(\mathbb {M}_r\) into G. In the case \(r=1\), we further identify the cohomological support variety of a finite-dimensional G-supermodule M as a subset of \(\mathscr {N}_1(G)\). We then discuss how our methods, when combined with recently announced results by Benson, Iyengar, Krause, and Pevtsova, can be applied to extend the homeomorphism \(\mathscr {N}_r(G)\simeq \left| G \right| \) to arbitrary infinitesimal unipotent supergroup schemes.
Kauffman states, bordered algebras, and a bigraded knot invariant

Abstract We define and study a bigraded knot invariant whose Euler characteristic is the Alexander polynomial, closely connected to knot Floer homology. The invariant is the homology of a chain complex whose generators correspond to Kauffman states for a knot diagram. The definition uses decompositions of knot diagrams: to a collection of points on the line, we associate a differential graded algebra; to a partial knot diagram, we associate modules over the algebra. The knot invariant is obtained from these modules by an appropriate tensor product.
A Proximal Jacobian ADMM Approach for Fast Massive MIMO Signal Detection in Low-Latency Communications

One of the 5G promises is to provide Ultra Reliable Low Latency Communications (URLLC) which targets an end to end communication latency that is &#x003C; 1ms. The very low latency requirement of URLLC entails a lot of work in all networking layers. In this paper, we focus on the physical layer, and in particular, we propose a novel formulation of the massive MIMO uplink detection problem. We introduce an objective function that is a sum of strictly convex and separable functions based on decomposing the received vector into multiple vectors. Each vector represents the contribution of one of the transmitted symbols in the received vector. Proximal Jacobian Alternating Direction Method of Multipliers (PJADMM) is used to solve the new formulated problem in an iterative manner where at every iteration all variables are updated in parallel and in a closed form expression. The proposed algorithm provides a lower complexity and much faster processing time compared to the conventional MMSE detection technique and other iterative-based techniques, especially when the number of single antenna users is close to the number of base station (BS) antennas. This improvement is obtained without any matrix inversion. Simulation results demonstrate the efficacy of the proposed algorithm in reducing detection processing time in the multi-user uplink massive MIMO setting.
Optimal function spaces for continuity of the Hessian determinant as a distribution

Abstract We establish optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on R N . In particular, inspired by recent work of Brezis and Nguyen on the distributional Jacobian determinant, we show that the action is continuous on the Besov space of fractional order B ( 2 − 2 N , N ) , and that all continuity results in this scale of Besov spaces are consequences of this result. A key ingredient in the argument is the characterization of B ( 2 − 2 N , N ) as the space of traces of functions in the Sobolev space W 2 , N ( R N + 2 ) on the subspace R N of codimension 2. The most delicate and elaborate part of the analysis is the construction of a counterexample to continuity in B ( 2 − 2 N , p ) with p > N .
A homotopy+ solution to the A-B slice problem

The A-B slice problem, a reformulation of the four-dimensional topological surgery conjecture for free groups, is shown to admit a link-homotopy+ solution. The proof relies on geometric applications of the group-theoretic 2-Engel relation. Implications for the surgery conjecture are discussed.
Isomorphic Busemann-Petty problem for sections of proportional dimensions

The main result of this note is a solution to the isomorphic Busemann-Petty problem for sections of proportional dimensions, as follows. Suppose that 0 < λ < 1 , k λ n , and K , L are origin-symmetric convex bodies in R n satisfying the inequalities | K ? H | ? | L ? H | , ? H ? Gr n - k , where Gr n - k is the Grassmanian of ( n - k ) -dimensional subspaces of R n , and | K | stands for volume of proper dimension. Then | K | n - k n ? C k ( ( 1 - log ? λ ) 3 λ ) k | L | n - k n , where C is an absolute constant.
Homogenization with Large Spatial Random Potential

We consider the homogenization of parabolic equations with large spatially dependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We characterize the leading effect in the random fluctuations and show that their spatial moments converge in law to Gaussian random variables. Both results hold for sufficiently small times and in sufficiently large spatial dimensions $d\geq\mathfrak{m}$, where $\mathfrak{m}$ is the order of the spatial pseudodifferential operator in the parabolic equation. In dimension $d<\mathfrak{m}$, the solution to the parabolic equation is shown to converge to the (nondeterministic) solution of a stochastic equation in [G. Bal, Comm. Math. Phys., 212 (2009), pp. 457–477]. The results are then extended to cover the case of long range random potentials, which generate larger, but still asymptotically Gaussian, random fluctuations.
Cyclic permutations realized by signed shifts

The periodic (ordinal) patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial characterization of the periodic patterns of an arbitrary signed shift, in terms of the structure of the descent set of a certain cyclic permutation associated to the pattern. Signed shifts are an important family of onedimensional dynamical systems that includes shift maps and the tent map as particular cases. Defined as a function on the set of infinite words on a finite alphabet, a signed shift deletes the first letter and, depending on its value, possibly applies the complementation operation on the remaining word. For shift maps, reverse shift maps, and the tent map, we give exact formulas for their number of periodic patterns. As a byproduct of our work, we recover results of Gessel– Reutenauer and Weiss–Rogers and obtain new enumeration formulas for pattern-avoiding cycles.
Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges

We provide a systematic study of non-Hermitian topologically charged systems, demonstrating that adding an arbitrary non-Hermitian perturbation transforms the Weyl points to one-dimensional exceptional contours, and can yield a topological phase transition.
Decentralized observability with limited communication between sensors

In this paper, we study the problem of jointly retrieving the state of a dynamical system, as well as the state of the sensors deployed to estimate it. We assume that the sensors possess a simple computational unit that is capable of performing simple operations, such as retaining the current state and model of the system in its memory.
Mixed cobinary trees

We develop basic cluster theory from an elementary point of view using a variation of binary trees which we call mixed cobinary trees (MCTs). We show that the number of isomorphism classes of such ...
Evidence of Government Subsidy on Mortgage Rate and Default: Revisited

Abstract I empirically evaluate the subsidized default insurance policy (implemented through the guarantee for government-sponsored enterprises) in the U.S. mortgage market. First, I find that the ...
Sequences with Low Correlation

Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in applications. We consider the problem of constructing pairs (f, g) of sequences such that both f and g have low mean square autocorrelation and f and g have low mean square mutual crosscorrelation. We focus on aperiodic correlation of binary sequences, and review recent contributions along with some historical context.
Regularity of solutions to degenerate p-Laplacian equations

Abstract We prove regularity results for solutions of the equation div ( 〈 A X u , X u 〉 p − 2 2 A X u ) = 0 , 1 p ∞ , where X = ( X 1 , … , X m ) is a family of vector fields satisfying Hormander’s condition, and A is an m × m symmetric matrix that satisfies degenerate ellipticity conditions. If the degeneracy is of the form λ w ( x ) 2 / p | ξ | 2 ≤ 〈 A ( x ) ξ , ξ 〉 ≤ Λ w ( x ) 2 / p | ξ | 2 , w ∈ A p , then we show that solutions are locally Holder continuous. If the degeneracy is of the form k ( x ) − 2 p ′ | ξ | 2 ≤ 〈 A ( x ) ξ , ξ 〉 ≤ k ( x ) 2 p | ξ | 2 , k ∈ A p ′ ∩ R H τ , where τ depends on the homogeneous dimension, then the solutions are continuous almost everywhere, and we give examples to show that this is the best result possible. We give an application to maps of finite distortion.
Scheduling Policies for Age Minimization in Wireless Networks with Unknown Channel State

Age of information (AoI) is a recently proposed metric that measures the time elapsed since the generation of the last received information update. We consider the problem of AoI minimization for a network under general interference constraints, and time varying channel. We study the case where the channel statistics are known, but the current channel state is unknown. We propose two scheduling policies, namely, the virtual queue based policy and age-based policy. In the virtual queue based policy, the scheduler schedules links with maximum weighted sum of the virtual queue lengths, while in the age-based policy, the scheduler schedules links with maximum weighted sum of a function of link AoI. We prove that the virtual queue based policy is peak age optimal, up to an additive constant, while the age-based policy is at most factor 4 away from the optimal age. Numerical results suggest that both the proposed policies are, in fact, very close to the optimal.
Propensity Score Weighting for Causal Inference with Clustered Data

Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-level covariates that are related to both the treatment assignment and outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a calibration technique for propensity score estimation under the latent ignorable treatment assignment mechanism, i. e., the treatment-outcome relationship is unconfounded given the observed covariates and the latent cluster-specific confounders. We impose novel balance constraints which imply exact balance of the observed confounders and the unobserved cluster-level confounders between the treatment groups. We show that the proposed calibrated propensity score weighting estimator is doubly robust in that it is consistent for the average treatment effect if either the propensity score model is correctly specified or the outcome follows a linear mixed effects model. Moreover, the proposed weighting method can be combined with sampling weights for an integrated solution to handle confounding and sampling designs for causal inference with clustered survey data. In simulation studies, we show that the proposed estimator is superior to other competitors. We estimate the effect of School Body Mass Index Screening on prevalence of overweight and obesity for elementary schools in Pennsylvania.
Distributed multi-task formation control under parametric communication uncertainties

Formation control is a key problem in the coordination of multiple agents. It arises new challenges to traditional formation control strategy when the communication among agents is affected by uncertainties. This paper considers the robust multi-task formation control problem of multiple nonpoint agents whose communications are disturbed by uncertain parameters. The control objectives include 1. achieving the desired configuration; 2. avoiding collisions; 3. preserving the connectedness of uncertain topology. To achieve these objectives, first, a condition of Linear Matrix Inequalities (LMIs) is proposed for checking the connectedness of uncertain topologies. Then, by preserving the initial topological connectedness, a gradient-based distributed controller is designed via Lyapunov-like barrier functions. Two numerical examples illustrate the effectiveness of the proposed method.
Complex Form of Classical and Quantum Electrodynamics

We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the corresponding differential balance equations are given. Conservation laws and quantization of the electromagnetic field will be discussed in this covariant approach elsewhere.
On the zeta function of divisors for projective varieties with higher rank divisor class group

Given a projective variety X defined over a finite field, the zeta function of divisors attempts to count all irreducible, codimension one subvarieties of X, each measured by their projective degree. When the dimension of X is greater than one, this is a purely p-adic function, convergent on the open unit disk. Four conjectures are expected to hold, the first of which is p-adic meromorphic continuation to all of Cp. When the divisor class group (divisors modulo linear equivalence) of X has rank one, then all four conjectures are known to be true. In this paper, we discuss the higher rank case. In particular, we prove a p-adic meromorphic continuation theorem which applies to a large class of varieties. Examples of such varieties are projective nonsingular surfaces defined over a finite field (whose effective monoid is finitely generated) and all projective toric varieties (smooth or singular).
Resilient Active Information Gathering with Mobile Robots

Applications of safety, security, and rescue in robotics, such as multi-robot target tracking, involve the execution of information acquisition tasks by teams of mobile robots. However, in failure-prone or adversarial environments, robots get attacked, their communication channels get jammed, and their sensors may fail, resulting in the withdrawal of robots from the collective task, and consequently the inability of the remaining active robots to coordinate with each other. As a result, traditional design paradigms become insufficient and, in contrast, resilient designs against system-wide failures and attacks become important. In general, resilient design problems are hard, and even though they often involve objective functions that are monotone or submodular, scalable approximation algorithms for their solution have been hitherto unknown. In this paper, we provide the first algorithm, enabling the following capabilities: minimal communication, i.e., the algorithm is executed by the robots based only on minimal communication between them; system-wide resiliency, i.e., the algorithm is valid for any number of denial-of-service attacks and failures; and provable approximation performance, i.e., the algorithm ensures for all monotone (and not necessarily submodular) objective functions a solution that is finitely close to the optimal. We quantify our algorithms approximation performance using a notion of curvature for monotone set functions. We support our theoretical analyses with simulated and real-world experiments, by considering an active information gathering scenario, namely, multi-robot target tracking.
Frontal cortex tracks surprise separately for different sensory modalities but engages a common inhibitory control mechanism

The brain constantly generates predictions about the environment to guide action. Unexpected events lead to surprise and can necessitate the modification of ongoing behavior. Surprise can occur for any sensory domain, but it is not clear how these separate surprise signals are integrated to affect motor output. By applying a trial-to-trial Bayesian surprise model to human electroencephalography data recorded during a cross-modal oddball task, we tested whether there are separate predictive models for different sensory modalities (visual, auditory), or whether expectations are integrated across modalities such that surprise in one modality decreases surprise for a subsequent unexpected event in the other modality. We found that while surprise was represented in a common frontal signature across sensory modalities (the fronto-central P3 event-related potential), the single-trial amplitudes of this signature more closely conformed to a model with separate surprise terms for each sensory domain. We then investigated whether surprise-related fronto-central P3 activity indexes the rapid inhibitory control of ongoing behavior after surprise, as suggested by recent theories. Confirming this prediction, the fronto-central P3 amplitude after both auditory and visual unexpected events was highly correlated with the fronto-central P3 found after stop-signals (measured in a separate stop-signal task). Moreover, surprise-related and stopping-related activity loaded onto the same component in a cross-task independent components analysis. Together, these findings suggest that medial frontal cortex maintains separate predictive models for different sensory domains, but engages a common mechanism for inhibitory control of behavior regardless of the source of surprise.