Targeted L1-Regularization and Joint Modeling of Neural Networks for Causal Inference

The calculation of the Augmented Inverse Probability Weighting (AIPW) estimator of the Average Treatment Effect (ATE) is carried out in two steps, where in the first step, the treatment and outcome are modeled, and in the second step, the predictions are inserted into the AIPW estimator. The model misspecification in the first step has led researchers to utilize Machine Learning algorithms instead of parametric algorithms. However, the existence of strong confounders and/or Instrumental Variables (IVs) can lead the complex ML algorithms to provide perfect predictions for the treatment model which can violate the positivity assumption and elevate the variance of AIPW estimators. Thus the complexity of ML algorithms must be controlled to avoid perfect predictions for the treatment model while still learning the relationship between the confounders and the treatment and outcome. We use two NN architectures with an L1-regularization on specific NN parameters and investigate how their certain hyperparameters should be tuned in the presence of confounders and IVs to achieve a low bias-variance tradeoff for ATE estimators such as AIPW estimator. Through simulation results, we will provide recommendations as to how NNs can be employed for ATE estimation.     

Robust AOA-Based Target Localization for Uniformly Distributed Noise via ℓp-ℓ1 Optimization

This paper addresses the problem of robust angle of arrival (AOA) target localization in the presence of uniformly distributed noise which is modeled as the mixture of Laplacian distribution and uniform distribution. Motivated by the distribution of noise, we develop a localization model by using the ℓp-norm with 0≤p<2 as the measurement error and the ℓ1-norm as the regularization term. Then, an estimator for introducing the proximal operator into the framework of the alternating direction method of multipliers (POADMM) is derived to solve the convex optimization problem when 1≤p<2. However, when 0≤p<1, the corresponding optimization problem is nonconvex and nonsmoothed. To derive a convergent method for this nonconvex and nonsmooth target localization problem, we propose a smoothed POADMM estimator (SPOADMM) by introducing the smoothing strategy into the optimization model. Eventually, the proposed algorithms are compared with some state-of-the-art robust algorithms via numerical simulations, and their effectiveness in uniformly distributed noise is discussed from the perspective of root-mean-squared error (RMSE). The experimental results verify that the proposed method has more robustness against outliers and is less sensitive to the selected parameters, especially the variance of the measurement noise.     

New Bounds and a Generalization for Share Conversion for 3-Server PIR

Private Information Retrieval (PIR) protocols, which allow the client to obtain data from servers without revealing its request, have many applications such as anonymous communication, media streaming, blockchain security, advertisement, etc. Multi-server PIR protocols, where the database is replicated among the non-colluding servers, provide high efficiency in the information-theoretic setting. Beimel et al. in CCC 12’ (further referred to as BIKO) put forward a paradigm for constructing multi-server PIR, capturing several previous constructions for k≥3 servers, as well as improving the best-known share complexity for 3-server PIR. A key component there is a share conversion scheme from corresponding linear three-party secret sharing schemes with respect to a certain type of “modified universal” relation. In a useful particular instantiation of the paradigm, they used a share conversion from (2,3)-CNF over Zm to three-additive sharing over Zpβ for primes p1,p2,p where p1≠p2 and m=p1·p2, and the relation is modified universal relation CSm. They reduced the question of the existence of the share conversion for a triple (p1,p2,p) to the (in)solvability of a certain linear system over Zp, and provided an efficient (in m,logp) construction of such a sharing scheme. Unfortunately, the size of the system is Θ(m2) which entails the infeasibility of a direct solution for big m’s in practice. Paskin-Cherniavsky and Schmerler in 2019 proved the existence of the conversion for the case of odd p1, p2 when p=p1, obtaining in this way infinitely many parameters for which the conversion exists, but also for infinitely many of them it remained open. In this work, using some algebraic techniques from the work of Paskin-Cherniavsky and Schmerler, we prove the existence of the conversion for even m’s in case p=2 (we computed β in this case) and the absence of the conversion for even m’s in case p>2. This does not improve the concrete efficiency of 3-server PIR; however, our result is promising in a broader context of constructing PIR through composition techniques with k≥3 servers, using the relation CSm where m has more than two prime divisors. Another our suggestion about 3-server PIR is that it’s possible to achieve a shorter server’s response using the relation CSm′ for extended Sm′⊃Sm. By computer search, in BIKO framework we found several such sets for small m’s which result in share conversion from (2,3)-CNF over Zm to 3-additive secret sharing over Zpβ′, where β′>0 is several times less than β, which implies several times shorter server’s response. We also suggest that such extended sets Sm′ can result in better PIR due to the potential existence of matching vector families with the higher Vapnik-Chervonenkis dimension.     

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification

Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (MFuzzyEn2D and MDispEn2D, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both MFuzzyEn2D and MDispEn2D approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover, MFuzzyEn2D results in a better classification performance than that extracted by MDispEn2D as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis.     

Pairwise Elastic Net Representation-Based Classification for Hyperspectral Image Classification

The representation-based algorithm has raised a great interest in hyperspectral image (HSI) classification. l1-minimization-based sparse representation (SR) attempts to select a few atoms and cannot fully reflect within-class information, while l2-minimization-based collaborative representation (CR) tries to use all of the atoms leading to mixed-class information. Considering the above problems, we propose the pairwise elastic net representation-based classification (PENRC) method. PENRC combines the l1-norm and l2-norm penalties and introduces a new penalty term, including a similar matrix between dictionary atoms. This similar matrix enables the automatic grouping selection of highly correlated data to estimate more robust weight coefficients for better classification performance. To reduce computation cost and further improve classification accuracy, we use part of the atoms as a local adaptive dictionary rather than the entire training atoms. Furthermore, we consider the neighbor information of each pixel and propose a joint pairwise elastic net representation-based classification (J-PENRC) method. Experimental results on chosen hyperspectral data sets confirm that our proposed algorithms outperform the other state-of-the-art algorithms.     

First-principles materials design of CuInSe2-based high-efficiency photovoltaic solar cells

Based on ab initio   electronic structure calculations by self-interaction-corrected local-density-approximation (SIC-LDA) with the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA), we propose a materials design for high efficiency photovoltaic solar cells (PVSCs). It is shown that (i) the concentration dependence of the mixing energy of CuIn_1−xGa_xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Ga}}_x{\mathrm{Se}}_2$ shows upward convexity, thus this system favors phase separation. Due to the type II band alignment between CuInSe₂${\mathrm{CuInSe}}_2$ and CuGaSe₂${\mathrm{CuGaSe}}_2$, efficient electron–hole separation is realized in decomposed phase of this system. (ii) CuIn_1−xZn_0.5xSn_0.5xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Zn}}_{0.5x}{\mathrm{Sn}}_{0.5x}{\mathrm{Se}}_2$ has a direct band gap and no impurity state appears in the gap. Therefore, cost reduction is possible by using Zn and Sn instead of In. (iii) n-type CuAl_1−xSn_xS₂${\mathrm{CuAl}}_{1-x}{\mathrm{Sn}}_x{\mathrm{S}}_2$ and p-type Cu_1−xV_CuxAlS₂${\mathrm{Cu}}_{1-x}{\mathrm{V}}_{\mathrm{Cu}x}{\mathrm{AlS}}_2$ have negative activation energy for doped impurities and are expected to be low-resistive transparent conducting sulfides, which should be useful for CuInSe₂${\mathrm{CuInSe}}_2$-based PVSCs.     

A Realization Approach to Lossy Network Compression of a Tuple of Correlated Multivariate Gaussian RVs

Examined in this paper is the Gray and Wyner source coding for a simple network of correlated multivariate Gaussian random variables, Y1:Ω→Rp1 and Y2:Ω→Rp2. The network consists of an encoder that produces two private rates R1 and R2, and a common rate R0, and two decoders, where decoder 1 receives rates (R1,R0) and reproduces Y1 by Y^1, and decoder 2 receives rates (R2,R0) and reproduces Y2 by Y^2, with mean-square error distortions E||Yi−Y^i||Rpi2≤Δi∈[0,∞],i=1,2. Use is made of the weak stochastic realization and the geometric approach of such random variables to derive test channel distributions, which characterize the rates that lie on the Gray and Wyner rate region. Specific new results include: (1) A proof that, among all continuous or finite-valued random variables, W:Ω→W, Wyner’s common information, C(Y1,Y2)=infPY1,Y2,W:PY1,Y2|W=PY1|WPY2|WI(Y1,Y2;W), is achieved by a Gaussian random variable, W:Ω→Rn of minimum dimension n, which makes the two components of the tuple (Y1,Y2) conditionally independent according to the weak stochastic realization of (Y1,Y2), and a the formula where di∈(0,1),i=1,…,n are the canonical correlation coefficients of the correlated parts of Y1 and Y2, and a realization of (Y1,Y2,W) which achieves this. (2) The parameterization of rates that lie on the Gray and Wyner rate region, and several of its subsets. The discussion is largely self-contained and proceeds from first principles, while connections to prior literature is discussed.     

Theory of twist liquids: Gauging an anyonic symmetry

Topological phases in (2+1)$(2+1)$-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric–magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids  , which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the Z₂${\mathbb{Z}}_2$-symmetric toric code, SO(2N)₁$SO{\left(2N\right)}_1$ and SU(3)₁$SU{\left(3\right)}_1$ state as well as the S₃$S_3$-symmetric SO(8)₁$SO{\left(8\right)}_1$ state and a non-Abelian chiral state we call the “4-Potts” state.     

Conductance oscillations in a mesoscopic ring threaded by a harmonically time-dependent magnetic flux

We consider a microscopic model for a one-dimensional ring of non-interacting electrons threaded by a magnetic flux of the form Φ(t)=Φ₀+Φ₁cos(Ω₀t)$\Phi (t)={\Phi }_0+{\Phi }_1\cos ({\Omega }_{0}t)$. The ring is attached to two reservoirs at which a bias voltage is applied. We focus on small amplitudes of Φ₁${\Phi }_1$, and we analyze the behavior of the conductance as a function of Φ₀${\Phi }_0$. We solve the problem by means of non-equilibrium Green function techniques.     

Effects of Gd substitution on the structural and magnetic properties of strontium hexaferrites

The effect of Gd substitution in M-type strontium hexaferrites has been examined in two series of samples, (_Sr1-xGdx)O·5.25$({\mathrm{Sr}}_{1-x}{\mathrm{Gd}}_x)\mathrm{O}·5.25$_Fe2O3${\mathrm{Fe}}_2{\mathrm{O}}_3$ and _{Sr1-xGdxFe12-xCoxO19}${\mathrm{Sr}}_{1-x}{\mathrm{Gd}}_x{\mathrm{Fe}}_{12-x}{\mathrm{Co}}_x{\mathrm{O}}_{19}$, both prepared by the ceramic method, where x=0–0.40$x=0–0.40$. The samples have been characterized by XRD, VSM and SEM-EDAX techniques. All substituted samples present primarily the hexaferrite structure. Sample (_{Sr0.95Gdx0.05})O·5.25$({\mathrm{Sr}}_{0.95}{\mathrm{Gd}}_{x0.05})\mathrm{O}·5.25$_Fe2O3${\mathrm{Fe}}_2{\mathrm{O}}_3$ is single phase. Formation of impurity phases is affected by stoichiometry and presence of Co. In Sr–Gd samples, coercivity showed a maximum value of 305 kA/m (3.8 kOe) for x=0.20$x=0.20$, while remanence and saturation magnetization did not decrease. Coercivity and magnetization in the Sr–Gd–Co series decreased steadily with substitution degree.     

Exchange bias of mu-metal thin films

The exchange bias of the soft ferromagnet mu-metal, _{Ni77Fe14Cu5Mo4}${\mathrm{Ni}}_{77}{\mathrm{Fe}}_{14}{\mathrm{Cu}}_5{\mathrm{Mo}}_4$, with the metallic antiferromagnet _Fe50Mn50${\mathrm{Fe}}_{50}{\mathrm{Mn}}_{50}$ has been studied as a function of ferromagnet thickness and buffer layer material. Mu-metal exhibits classic exchange bias behavior: the exchange bias (_HEB)$(H_{\mathit{EB}})$ and coercive fields scale inversely with the ferromagnet's thickness, with H_EB varying as the cosine of the in-plane applied field angle. Ta buffers, rather than Cu, allow the mu-metal to retain more of its soft magnetic character while exhibiting exchange bias. The ability to preserve soft ferromagnetic behavior in an exchange biased heterostructure may be useful for low field sensing and other device applications.     

On the propensity of magnetism in 3d transition-metal-MgCNi3 alloys

The effects of disorder and incipient magnetism in MgC(_Ni1-xTx)3$\mathrm{MgC}({\mathrm{Ni}}_{1-x}{\mathrm{T}}_x{)}_3$ (T≡Fe$\mathrm{T}\equiv \mathrm{Fe}$, Co or Cu) alloys are studied using coherent-potential approximation and Ginzburg–Landau coefficients. The first-principles, local-density-functional-based calculations for substitutionally disordered Fe and Co impurities in the Ni sub-lattice of MgCNi₃, in low concentrations, show that incipient magnetism resides in these materials. The overestimation of the calculated magnetic properties points to the limitations of the local-density approximation. However, using a phenomenological approach based on Ginzburg–Landau coefficients and the fixed-spin moment method, we show that MgC(_Ni1-xTx)3$\mathrm{MgC}({\mathrm{Ni}}_{1-x}{\mathrm{T}}_x{)}_3$ alloys remain paramagnetic. At expanded volumes, we also find the possibility of a ferromagnetic state for MgC(_{Ni0.95Fe0.05)3}$\mathrm{MgC}({\mathrm{Ni}}_{0.95}{\mathrm{Fe}}_{0.05}{)}_3$ and MgC(_{Ni0.90Co0.10)3}$\mathrm{MgC}({\mathrm{Ni}}_{0.90}{\mathrm{Co}}_{0.10}{)}_3$ alloys.     

Lower Bounds on Multivariate Higher Order Derivatives of Differential Entropy

This paper studies the properties of the derivatives of differential entropy H(Xt) in Costa’s entropy power inequality. For real-valued random variables, Cheng and Geng conjectured that for m≥1, (−1)m+1(dm/dtm)H(Xt)≥0, while McKean conjectured a stronger statement, whereby (−1)m+1(dm/dtm)H(Xt)≥(−1)m+1(dm/dtm)H(XGt). Here, we study the higher dimensional analogues of these conjectures. In particular, we study the veracity of the following two statements: C1(m,n):(−1)m+1(dm/dtm)H(Xt)≥0, where n denotes that Xt is a random vector taking values in Rn, and similarly, C2(m,n):(−1)m+1(dm/dtm)H(Xt)≥(−1)m+1(dm/dtm)H(XGt)≥0. In this paper, we prove some new multivariate cases: C1(3,i),i=2,3,4. Motivated by our results, we further propose a weaker version of McKean’s conjecture C3(m,n):(−1)m+1(dm/dtm)H(Xt)≥(−1)m+11n(dm/dtm)H(XGt), which is implied by C2(m,n) and implies C1(m,n). We prove some multivariate cases of this conjecture under the log-concave condition: C3(3,i),i=2,3,4 and C3(4,2). A systematic procedure to prove Cl(m,n) is proposed based on symbolic computation and semidefinite programming, and all the new results mentioned above are explicitly and strictly proved using this procedure.     

A model with two inert scalar doublets

We consider an extension of the standard model (SM) with three SU(2)$SU\left(2\right)$ scalar doublets and discrete S₃⊗Z₂$S_3\otimes {\mathbb{Z}}_2$ symmetries. The irreducible representation of S₃$S_3$ has a singlet and a doublet, and here we show that the singlet corresponds to the SM-like Higgs and the two additional SU(2)$SU\left(2\right)$ doublets forming a S₃$S_3$ doublet are inert. In general, in a three scalar doublet model, with or without S₃$S_3$ symmetry, the diagonalization of the mass matrices implies arbitrary unitary matrices. However, we show that in our model these matrices are of the tri-bimaximal type. We also analyzed the scalar mass spectra and the conditions for the scalar potential is bounded from below at the tree level. We also discuss some phenomenological consequences of the model.     

The analytic solution for the power series expansion of Heun function

The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric ₂F₁${}_2{F}_1$, ₁F₁${}_1{F}_1$ and ₀F₁${}_0{F}_1$ functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins.     

Effects of colored noise and noise delay on a calcium oscillation system

As a calcium oscillations system is in steady state, the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods. The results indicate that: (1) the colored noise can induce coherence bi-resonance phenomenon. (2) there exist three peaks in the R–_τ0$R\text{–}{\tau }_0$ (R$R$ is the reciprocal coefficient of variance, and _τ0${\tau }_0$ is the self-correlation time of the colored noise) curves. For the same noise intensity Q=1$Q=1$, the Gaussian colored noise can induce calcium spikes but the white noise cannot do this. (3) the delay time can improve noise induced spikes regularity as _τ0${\tau }_0$ is small, and R$R$ has a significant minimum with increasing τ$\tau$ as _τ0${\tau }_0$ is large. (4) large values of ζ$\zeta$ reduce noise induced spikes regularity.