Naive Construction Research Articles

Multi-Sensor Joint Adaptive Birth Sampler for Labeled Random Finite Set Tracking

This paper provides a scalable, multi-sensor measurement adaptive track initiation technique for labeled random finite set filters. A naive construction of the multi-sensor measurement adaptive birth set distribution leads to an exponential number of newborn components in the number of sensors. A truncation criterion is established for a labeled multi-Bernoulli random finite set birth density. The proposed truncation criterion is shown to have a bounded L1 error in the generalized labeled multi-Bernoulli posterior density. This criterion is used to construct a Gibbs sampler that produces a truncated measurement-generated labeled multi-Bernoulli birth distribution with quadratic complexity in the number of sensors. A closed-form solution of the conditional sampling distribution assuming linear Gaussian likelihoods is provided, alongside an approximate solution using Monte Carlo importance sampling. Multiple simulation results are provided to verify the efficacy of the truncation criterion, as well as the reduction in complexity.

On XOR lemmas for the weight of polynomial threshold functions

A multilinear polynomial p is said to sign-represent a Boolean function f:{−1,1}n→{−1,1} if f(x)=sgn(p(x)) for all x∈{−1,1}n. In this paper, we consider the length and weight of polynomials sign-representing Boolean functions of the form ⊕kf, the XOR of k copies of f on disjoint sets of variables.Firstly, we show that for an infinite family of functions f, a naive construction does not yield a shortest polynomial sign-representing ⊕kf. More precisely, we give a construction of polynomials sign-representing ⊕kANDn whose length is strictly smaller than the k-th power of the minimum length of a polynomial sign-representing ANDn, for every k≥2 and n≥2 except for k=n=2. Previously, such polynomials were known only for n=2 (Sezener and Oztop, 2015). A similar result for the weight is also provided. Secondly, we introduce a parameter vf⁎ of a Boolean function f and show that the k-th root of the minimum weight of a polynomial sign-representing ⊕kf converges between vf⁎ and (vf⁎)2 as k goes to infinity.

Query-Adaptive Reciprocal Hash Tables for Nearest Neighbor Search.

Recent years have witnessed the success of binary hashing techniques in approximate nearest neighbor search. In practice, multiple hash tables are usually built using hashing to cover more desired results in the hit buckets of each table. However, rare work studies the unified approach to constructing multiple informative hash tables using any type of hashing algorithms. Meanwhile, for multiple table search, it also lacks of a generic query-adaptive and fine-grained ranking scheme that can alleviate the binary quantization loss suffered in the standard hashing techniques. To solve the above problems, in this paper, we first regard the table construction as a selection problem over a set of candidate hash functions. With the graph representation of the function set, we propose an efficient solution that sequentially applies normalized dominant set to finding the most informative and independent hash functions for each table. To further reduce the redundancy between tables, we explore the reciprocal hash tables in a boosting manner, where the hash function graph is updated with high weights emphasized on the misclassified neighbor pairs of previous hash tables. To refine the ranking of the retrieved buckets within a certain Hamming radius from the query, we propose a query-adaptive bitwise weighting scheme to enable fine-grained bucket ranking in each hash table, exploiting the discriminative power of its hash functions and their complement for nearest neighbor search. Moreover, we integrate such scheme into the multiple table search using a fast, yet reciprocal table lookup algorithm within the adaptive weighted Hamming radius. In this paper, both the construction method and the query-adaptive search method are general and compatible with different types of hashing algorithms using different feature spaces and/or parameter settings. Our extensive experiments on several large-scale benchmarks demonstrate that the proposed techniques can significantly outperform both the naive construction methods and the state-of-the-art hashing algorithms.

Differentially-private learning of low dimensional manifolds

In this paper, we study the problem of differentially-private learning of low dimensional manifolds embedded in high dimensional spaces. The problems one faces in learning in high dimensional spaces are compounded in a differentially-private learning. We achieve the dual goals of learning the manifold while maintaining the privacy of the dataset by constructing a differentially-private data structure that adapts to the doubling dimension of the dataset. Our differentially-private manifold learning algorithm extends random projection trees of Dasgupta and Freund. A naive construction of differentially-private random projection trees could involve queries with high global sensitivity that would affect the usefulness of the trees. Instead, we present an alternate way of constructing differentially-private random projection trees that uses low sensitivity queries that are precise enough for learning the low dimensional manifolds. We prove that the size of the tree depends only on the doubling dimension of the dataset and not its extrinsic dimension.

First, second, and third order finite-volume schemes for advection–diffusion

In this paper, we present first, second, and third order implicit finite-volume solvers for advection–diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate third-order advection–diffusion scheme is made trivial by the hyperbolic method while a naive construction of adding a third-order diffusion scheme to a third-order advection scheme can fail to yield third-order accuracy. We demonstrate also that the gradients are computed simultaneously to the same order of accuracy as that of the solution variable on irregular triangular grids: first, second and third order accurate gradients by the first, second, and third order schemes, respectively. Furthermore, the first and second order schemes are shown to achieve one order higher accuracy for the solution variable in the advection limit. It is also shown that these schemes are capable of producing highly accurate and smooth solution gradients along the boundary in a highly-skewed anisotropic irregular triangular grid while conventional schemes suffer from oscillations on such a grid. Numerical results show that these schemes are capable of delivering high accuracy over conventional schemes at a significantly reduced cost.

A Survey of Low Volatility Strategies

This paper replicates various low volatility strategies and examines their historical performance using U.S., global developed markets, and emerging markets data. In our sample, low volatility strategies outperformed their corresponding cap-weighted market indices due to exposure to the value, betting against beta (BAB), and duration factors. (The duration factor introduced here is new to the low volatility literature.) The reduction in volatility is driven by a substantial reduction in the portfolios’ market beta. For long-term investors, low volatility strategies can contribute to a more risk-diversified equity portfolio which earns equity returns from multiple premium sources instead of market beta alone. Nonetheless, while the lower risk and higher return seem persistent and robust across geographies and over time, we find flaws with naive constructions of low volatility portfolios. First, naive low volatility strategies tend to have very high turnover and low liquidity, which can erode returns significantly. They also have very concentrated country/industry allocations, which neither provide sensible economic exposures nor find theoretical support in the more recent literature on the within-country/industry low volatility effect. Additionally, there is concern that low volatility stocks could become expensive, a development which would eliminate their performance advantage. Portfolio construction methods should be sensitive to valuation levels and investability.

Wrinkles as the Result of Compressive Stresses in an Annular Thin Film

It is well‐known that an elastic sheet loaded in tension will wrinkle and that the length scale of the wrinkles tends to 0 with vanishing thickness of the sheet [Cerda and Mahadevan, Phys. Rev. Lett. 90, 074302 (2003)]. We give the first mathematically rigorous analysis of such a problem. Since our methods require an explicit understanding of the underlying (convex) relaxed problem, we focus on the wrinkling of an annular sheet loaded in the radial direction [Davidovitch et al., Proc. Natl. Acad. Sci. 108 (2011), 18227]. Our main achievement is identification of the scaling law of the minimum energy as the thickness of the sheet tends to 0. This requires proving an upper bound and a lower bound that scale the same way. We prove both bounds first in a simplified Kirchhoff‐Love setting and then in the nonlinear three‐dimensional setting. To obtain the optimal upper bound, we need to adjust a naive construction (one family of wrinkles superimposed on a planar deformation) by introducing a cascade of wrinkles. The lower bound is more subtle, since it must be ansatz‐free. © 2014 Wiley Periodicals, Inc.

Microscopic Model of Quasiparticle Wave Packets in Superfluids, Superconductors, and Paired Hall States

We study the structure of Bogoliubov quasiparticles, bogolons, the fermionic excitations of paired superfluids that arise from fermion (BCS) pairing, including neutral superfluids, superconductors, and paired quantum Hall states. The naive construction of a stationary quasiparticle in which the deformation of the pair field is neglected leads to a contradiction: it carries a net electrical current even though it does not move. However, treating the pair field self-consistently resolves this problem: in a neutral superfluid, a dipolar current pattern is associated with the quasiparticle for which the total current vanishes. When Maxwell electrodynamics is included, as appropriate to a superconductor, this pattern is confined over a penetration depth. For paired quantum Hall states of composite fermions, the Maxwell term is replaced by a Chern-Simons term, which leads to a dipolar charge distribution and consequently to a dipolar current pattern.

Covariant Closed String Coherent States

We give the first construction of covariant coherent closed string states, which may be identified with fundamental cosmic strings. We outline the requirements for a string state to describe a cosmic string, and provide an explicit and simple map that relates three different descriptions: classical strings, light cone gauge quantum states, and covariant vertex operators. The resulting coherent state vertex operators have a classical interpretation and are in one-to-one correspondence with arbitrary classical closed string loops.

Erratum: SpontaneousCPviolation inE6supersymmetric grand unified theory with SU(2) flavor and anomalous U(1) symmetries [Phys. Rev. D80, 115011 (2009)

We construct a model of spontaneous CP violation in E6 supersymmetric grand unified theory. In the model, we employ an SU(2)F flavor symmetry and an anomalous U(1)A symmetry. The SU(2)F flavor symmetry is introduced to provide the origin of hierarchical structures of Yukawa coupling and to ensure the universality of sfermion soft masses. The anomalous U(1)A symmetry is introduced to realize the doublet-triplet mass splitting, to provide the origin of hierarchical structures of Yukawa couplings, and to solve the mu problem. In the model, CP is spontaneously broken by the SU(2)F breaking in order to provide a Kobayashi-Maskawa phase and to evade the supersymmetric CP problem. However, a naive construction of the model generally leads to unwanted outcome, Arg[mu b*]=O(1), when CP violating effects in the flavor sector are taken into account. We cure this difficulty by imposing a discrete symmetry and find that this prescription can play additional roles. It ensures that realistic up-quark mass and Cabibbo angle are simultaneously realized without cancellation between O(1) coefficients. Also, severe constraints from the chromo-electric dipole moment of the quark can be satisfied without destabilizing the weak scale. The discrete symmetry reduces the number of free parameters, but the model is capable of reproducing quark and lepton mass spectra, mixing angles, and a Jarlskog invariant. We obtain characteristic predictions Vub sim O(lambda^4) (lambda=0.22) and |Vcb Yb| = |Yc| at the grand unified theory scale.

SpontaneousCPviolation inE6supersymmetric grand unified theory with SU(2) flavor and anomalous U(1) symmetries

We construct a model of spontaneous $CP$ violation in ${\mathrm{E}}_{6}$ supersymmetric grand unified theory. In the model, we employ an $\mathrm{SU}(2{)}_{\mathrm{F}}$ flavor symmetry and an anomalous $\mathrm{U}(1{)}_{\mathrm{A}}$ symmetry. The $\mathrm{SU}(2{)}_{\mathrm{F}}$ flavor symmetry is introduced to provide the origin of hierarchical structures of Yukawa coupling and to ensure the universality of sfermion soft masses. The anomalous $\mathrm{U}(1{)}_{\mathrm{A}}$ symmetry is introduced to realize the doublet-triplet mass splitting, to provide the origin of hierarchical structures of Yukawa couplings, and to solve the $\ensuremath{\mu}$ problem. In the model, $CP$ is spontaneously broken by the $\mathrm{SU}(2{)}_{\mathrm{F}}$ breaking in order to provide a Kobayashi-Maskawa phase and to evade the supersymmetric $CP$ problem. However, a naive construction of the model generally leads to an unwanted outcome, $\mathrm{arg}[\ensuremath{\mu}{b}^{*}]=\mathcal{O}(1)$, when $CP$ violating effects in the flavor sector are taken into account. We cure this difficulty by imposing a discrete symmetry and find that this prescription can play additional roles. It ensures that the realistic up-quark mass and Cabibbo angle are simultaneously realized without cancellation between $\mathcal{O}(1)$ coefficients. Also, severe constraints from the chromo-electric dipole moment of the quark can be satisfied without destabilizing the weak scale. The discrete symmetry reduces the number of free parameters, but the model is capable of reproducing quark and lepton mass spectra, mixing angles, and a Jarlskog invariant. We obtain characteristic predictions ${V}_{ub}\ensuremath{\sim}\mathcal{O}({\ensuremath{\lambda}}^{4})$ ($\ensuremath{\lambda}=0.22$) and $|{V}_{cb}{Y}_{b}|=|{Y}_{c}|$ at the grand unified theory scale.

Estimating the parameters of the operational model of pharmacological agonism

The aim of this work is practical. We show that the parameters of the widely used operational model of pharmacological agonism are difficult to estimate from single dose-response curves. The parameters can be estimated using pairs of dose-response curves (usually treatment and control) sharing some parameters. Confidence bands for the estimators are developed. In the case of multiple dose-response curve pairs one can employ a non-linear mixed effects model to allow for inter-individual variation. The point estimates and the confidence intervals thus obtained are similar to the more naive construction based on mean and standard errors of parameter estimates. To test for difference of certain parameters between treatment and control we employ a permutation test and Wald's test.

Taste breaking in staggered fermions from random matrix theory

Abstract We discuss the construction of a chiral random matrix model for staggered fermions. This model includes O(a2) corrections to the continuum limit of staggered fermions and is related to the zero momentum limit of the Lee-Sharpe Lagrangian for staggered fermions. The naive construction based on a specific expansion in lattice spacing (a) of the Dirac matrix produces the term which gives the dominant contribution to the observed taste splitting in the pion masses. A more careful analysis can include extra terms which are also consistent with the symmetries of staggered fermions. Lastly I will mention possible uses of the model including studies of topology and fractional powers of the fermion determinant.

Vortex fermion on the lattice

The domain wall fermion formalism in lattice gauge theory is much investigated recently. This is set up by reducing (4+1)-dimensional theory to low energy effective 4-dimensional one. In order to look around other possibilities of realizing chiral fermion on the lattice, we construct vortex fermion by reducing (4+2)-dimensional theory to low energy effective 4-dimensional one on the lattice. In extra 2 dimensions we propose a new lattice regularization which has a discrete rotational invariance but not a translational one. In order to eliminate doubling species in the naive construction we introduce the extended Wilson term which is appropriate to our model. We propose two models for convenience and show that a normalizable zero mode solution appears at the core of the vortex.

Some naive constructions of S(2, 3, v) and S(2, 4, v)

De Resmini, M.J., Some naive constructions of S(2, 3, u) and S(2, 4, u), Discrete Mathematics 97 (1991) 149-1.53. The aim of this paper is to present some very easy constructions of S(2, 3, V)‘S and S(2, 4, V)‘S which yield Steiner systems containing three and four prescribed subsystems respectively, and possibly admitting a partition into those subsystems. Furthermore, the subsystems of the obtained new Steiner systems are only the given ones and their possible subsystems. We assume the reader is familiar with the Steiner system terminology and refer him or her to [l, 81 for background and to [6-71 for literature on the subject. A well-known theorem of Doyen [5] states that, given three STS’s 4, i = 1, 2, 3, of the same order u sharing precisely one, possibly empty, subsystem of order w, it is possible to construct an STS of order 3(v w) + w whose only subsystems are the Si’s. Here we consider two naive special cases of Doyen’s construction for two motivations. First, one of these constructions, namely Construction 2, can always be used to produce an S(2, 3, 3(2, w) + w) when the three starting STS(v)‘s share precisely one subsystem of order w 2 0. Secondly, a suitable combination of the two constructions yields a construction of an S(2, 4, 4(v w) + w) by starting with four S(2, 4, V)‘S sharing exactly one, possibly empty, subsystem of order w under the condition v w s 1 (mod 2). In particular, when the four given systems share precisely one point, we obtain an S(2, 4, 4(v 1) + 1) containing the given systems of order v provided that v = 4 (mod 12). Construction 1. This construction of Steiner triple systems works only when the three starting STS(v)‘s are mutually disjoint. Therefore, the obtained STS(3u) admits a partition into three subsystems. 0012-365X/91/$03.50