Time-shift replacement algorithm for main memory performance optimization

Page replacement algorithms of main memory in modern operating systems are crucial in system performance. When memory is full, a page replacement algorithm exploits temporal locality and frequency of page references to evict the page that is least likely to be accessed in the near future. Subsequently, loading the majority of data directly from memory improves performance by reducing I/O waits of accessing slow storage. Research of replacement algorithms that maximizes hit ratio while incurring as less overhead as possible has been constantly studied. In this paper, we propose a time-shift least recently used (TSLRU) algorithm that converts frequency information of page references into temporal locality. Frequent accesses of a page are thus recognized and accumulated in terms of time. Moreover, pages being loaded into memory for the first time are not necessarily the most recently used pages. As a result, one-pass pages are evicted sooner in our algorithm than in traditional LRU algorithm. Our performance evaluations show that the TSLRU outperforms conventional page replacement algorithms on both artificial and real application traces. For example, hit ratio of TSLRU advances ARC by \(4.17\%\) and LRU by \(5.91\%\) on normal distributed workloads. Moreover, TSLRU outperforms ARC by over \(2\%\) on half of the application traces tested.     

Characteristics of social media stories

An emerging trend in social media is for users to create and publish “stories”, or curated lists of  Web resources, with the purpose of creating a particular narrative of interest to the user. While some stories on the Web are automatically generated, such as Facebook’s “Year in Review”, one of the most popular storytelling services is “Storify”, which provides users with curation tools to select, arrange, and annotate stories with content from social media and the Web at large. We would like to use tools, such as Storify, to present (semi-)automatically created summaries of archival collections. To support automatic story creation, we need to better understand as a baseline the structural characteristics of popular (i.e., receiving the most views) human-generated stories. We investigated 14,568 stories from Storify, comprising 1,251,160 individual resources, and found that popular stories (i.e., top 25 % of views normalized by time available on the Web) have the following characteristics: 2/28/1950 elements (min/median/max), a median of 12 multimedia resources (e.g., images, video), 38 % receive continuing edits, and 11 % of their elements are missing from the live Web. We also checked the population of Archive-It collections (3109 collections comprising 305,522 seed URIs) for better understanding the characteristics of the collections that we intend to summarize. We found that the resources in human-generated stories are different from the resources in Archive-It collections. In summarizing a collection, we can only choose from what is archived (e.g., twitter.com is popular in Storify, but rare in Archive-It). However, some other characteristics of human-generated stories will be applicable, such as the number of resources.     

New q-ary quantum MDS codes with distances bigger than $$\frac{ q}{2}$$

The construction of quantum MDS codes has been studied by many authors. We refer to the table in page 1482 of (IEEE Trans Inf Theory 61(3):1474–1484, 2015) for known constructions. However, there have been constructed only a few q-ary quantum MDS \([[n,n-2d+2,d]]_q\) codes with minimum distances \(d>\frac{q}{2}\) for sparse lengths \(n>q+1\). In the case \(n=\frac{q^2-1}{m}\) where \(m|q+1\) or \(m|q-1\) there are complete results. In the case \(n=\frac{q^2-1}{m}\) while \(m|q^2-1\) is neither a factor of \(q-1\) nor \(q+1\), no q-ary quantum MDS code with \(d> \frac{q}{2}\) has been constructed. In this paper we propose a direct approach to construct Hermitian self-orthogonal codes over \(\mathbf{F}_{q^2}\). Then we give some new q-ary quantum codes in this case. Moreover many new q-ary quantum MDS codes with lengths of the form \(\frac{w(q^2-1)}{u}\) and minimum distances \(d > \frac{q}{2}\) are presented.     

Subspace Learning by $$\ell ^{0}$$-Induced Sparsity

Subspace clustering methods partition the data that lie in or close to a union of subspaces in accordance with the subspace structure. Such methods with sparsity prior, such as sparse subspace clustering (SSC) (Elhamifar and Vidal in IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781, 2013) with the sparsity induced by the \(\ell ^{1}\)-norm, are demonstrated to be effective in subspace clustering. Most of those methods require certain assumptions, e.g. independence or disjointness, on the subspaces. However, these assumptions are not guaranteed to hold in practice and they limit the application of existing sparse subspace clustering methods. In this paper, we propose \(\ell ^{0}\)-induced sparse subspace clustering (\(\ell ^{0}\)-SSC). In contrast to the required assumptions, such as independence or disjointness, on subspaces for most existing sparse subspace clustering methods, we prove that \(\ell ^{0}\)-SSC guarantees the subspace-sparse representation, a key element in subspace clustering, for arbitrary distinct underlying subspaces almost surely under the mild i.i.d. assumption on the data generation. We also present the “no free lunch” theorem which shows that obtaining the subspace representation under our general assumptions can not be much computationally cheaper than solving the corresponding \(\ell ^{0}\) sparse representation problem of \(\ell ^{0}\)-SSC. A novel approximate algorithm named Approximate \(\ell ^{0}\)-SSC (A\(\ell ^{0}\)-SSC) is developed which employs proximal gradient descent to obtain a sub-optimal solution to the optimization problem of \(\ell ^{0}\)-SSC with theoretical guarantee. The sub-optimal solution is used to build a sparse similarity matrix upon which spectral clustering is performed for the final clustering results. Extensive experimental results on various data sets demonstrate the superiority of A\(\ell ^{0}\)-SSC compared to other competing clustering methods. Furthermore, we extend \(\ell ^{0}\)-SSC to semi-supervised learning by performing label propagation on the sparse similarity matrix learnt by A\(\ell ^{0}\)-SSC and demonstrate the effectiveness of the resultant semi-supervised learning method termed \(\ell ^{0}\)-sparse subspace label propagation (\(\ell ^{0}\)-SSLP).     

No nexiste nce of n-qubit u nexte ndible product bases of size $$2^ n-5$$2 n-5

It is known that the n-qubit system has no unextendible product bases (UPBs) of cardinality \(2^n-1\), \(2^n-2\) and \(2^n-3\). On the other hand, the n-qubit UPBs of cardinality \(2^n-4\) exist for all \(n\ge 3\). We prove that they do not exist for cardinality \(2^n-5\).     

Optimal noise functions for location privacy on continuous regions

Users of location-based services are highly vulnerable to privacy risks since they need to disclose, at least partially, their locations to benefit from these services. One possibility to limit these risks is to obfuscate the location of a user by adding random noise drawn from a noise function. In this paper, we require the noise functions to satisfy a generic location privacy notion called \(\ell \)-privacy, which makes the position of the user in a given region \(\mathcal {X}\) relatively indistinguishable from other points in \(\mathcal {X}\). We also aim at minimizing the loss in the service utility due to such obfuscation. While existing optimization frameworks regard the region \(\mathcal {X}\) restrictively as a finite set of points, we consider the more realistic case in which the region is rather continuous with a nonzero area. In this situation, we demonstrate that circular noise functions are enough to satisfy \(\ell \)-privacy on \(\mathcal {X}\) and equivalently on the entire space without any penalty in the utility. Afterward, we describe a large parametric space of noise functions that satisfy \(\ell \)-privacy on \(\mathcal {X}\), and show that this space has always an optimal member, regardless of \(\ell \) and \(\mathcal {X}\). We also investigate the recent notion of \(\epsilon \)-geo-indistinguishability as an instance of \(\ell \)-privacy and prove in this case that with respect to any increasing loss function, the planar Laplace noise function is optimal for any region having a nonzero area.     

Shrinking one-way cellular automata

We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata (\(\text{OCA}\)) with the additional property that during a computation any cell of the \(\text{OCA}\) has the ability to dissolve itself, so-called shrinking one-way cellular automata (\(\text{SOCA}\)). It turns out that real-time \(\text{SOCA}\) are more powerful than real-time \(\text{OCA}\), since they can accept certain linear-time \(\text{OCA}\) languages. On the other hand, linear-time \(\text{OCA}\) are more powerful than real-time \(\text{SOCA}\), which is witnessed even by a unary language. Additionally, a construction is provided that enables real-time \(\text{SOCA}\) to accept the reversal of real-time iterative array languages. Finally, restricted real-time \(\text{SOCA}\) are investigated. We distinguish two limitations for the dissolving of cells. One restriction is to bound the total number of cells that are allowed to dissolve by some function. In this case, an infinite strict hierarchy of language classes is obtained. The second restriction is inspired by an approach to limit the amount of nondeterminism in \(\text{OCA}\). Compared with the first restriction, the total number of cells that may dissolve is still unbounded, but the number of time steps at which a cell may dissolve is bounded. The possibility to dissolve is allowed only in the first k time steps, where \(k\ge 0\) is some constant. For this mode of operation an infinite, tight, and strict hierarchy of language classes is obtained as well.     

A greedy approximation algorithm for minimum-gap scheduling

We consider scheduling of unit-length jobs with release times and deadlines, where the objective is to minimize the number of gaps in the schedule. Polynomial-time algorithms for this problem are known, yet they are rather inefficient, with the best algorithm running in time \(O(n^4)\) and requiring \(O(n^3)\) memory. We present a greedy algorithm that approximates the optimum solution within a factor of 2 and show that our analysis is tight. Our algorithm runs in time \(O(n^2 \log n)\) and needs only O(n) memory. In fact, the running time is \(O(n (g^*+1)\log n)\), where \(g^*\) is the minimum number of gaps.     

On topological systems

We establish the reflectivity of the subcategories of \(T_{0}\) and sober topological systems in the category \(\mathbf {TopSys}\) of topological systems. We also introduce a Sierpinski object in the category \(\mathbf {TopSys}\) and point out its connection with \(T_{0}\) and sober topological systems and also with injective \(T_{0}\)-topological systems.     

Hybridized Discontinuous Galerkin Method for Elliptic Interface Problems: Error Estimates Under Low Regularity Assumptions of Solutions

New hybridized discontinuous Galerkin (HDG) methods for the interface problem for elliptic equations are proposed. Unknown functions of our schemes are \(u_h\) in elements and \(\hat{u}_h\) on inter-element edges. That is, we formulate our schemes without introducing the flux variable. We assume that subdomains \(\Omega _1\) and \(\Omega _2\) are polyhedral domains and that the interface \(\Gamma =\partial \Omega _1\cap \partial \Omega _2\) is polyhedral surface or polygon. Moreover, \(\Gamma \) is assumed to be expressed as the union of edges of some elements. We deal with the case where the interface is transversely connected with the boundary of the whole domain \(\overline{\Omega }=\overline{\Omega _1\cap \Omega _2}\). Consequently, the solution u of the interface problem may not have a sufficient regularity, say \(u\in H^2(\Omega )\) or \(u|_{\Omega _1}\in H^2(\Omega _1)\), \(u|_{\Omega _2}\in H^2(\Omega _2)\). We succeed in deriving optimal order error estimates in an HDG norm and the \(L^2\) norm under low regularity assumptions of solutions, say \(u|_{\Omega _1}\in H^{1+s}(\Omega _1)\) and \(u|_{\Omega _2}\in H^{1+s}(\Omega _2)\) for some \(s\in (1/2,1]\), where \(H^{1+s}\) denotes the fractional order Sobolev space. Numerical examples to validate our results are also presented.     

Fast L1–L2 Minimization via a Proximal Operator

This paper aims to develop new and fast algorithms for recovering a sparse vector from a small number of measurements, which is a fundamental problem in the field of compressive sensing (CS). Currently, CS favors incoherent systems, in which any two measurements are as little correlated as possible. In reality, however, many problems are coherent, and conventional methods such as \(L_1\) minimization do not work well. Recently, the difference of the \(L_1\) and \(L_2\) norms, denoted as \(L_1\)–\(L_2\), is shown to have superior performance over the classic \(L_1\) method, but it is computationally expensive. We derive an analytical solution for the proximal operator of the \(L_1\)–\(L_2\) metric, and it makes some fast \(L_1\) solvers such as forward–backward splitting (FBS) and alternating direction method of multipliers (ADMM) applicable for \(L_1\)–\(L_2\). We describe in details how to incorporate the proximal operator into FBS and ADMM and show that the resulting algorithms are convergent under mild conditions. Both algorithms are shown to be much more efficient than the original implementation of \(L_1\)–\(L_2\) based on a difference-of-convex approach in the numerical experiments.     

Ordering states with Tsallis relative $$\alpha $$-entropies of coherence

In this paper, we study the ordering states with Tsallis relative \(\alpha \)-entropies of coherence and \(l_{1}\) norm of coherence for single-qubit states. Firstly, we show that any Tsallis relative \(\alpha \)-entropies of coherence and \(l_{1}\) norm of coherence give the same ordering for single-qubit pure states. However, they do not generate the same ordering for some high-dimensional states, even though these states are pure. Secondly, we also consider three special Tsallis relative \(\alpha \)-entropies of coherence for \(\alpha =2, 1, \frac{1}{2}\) and show these three measures and \(l_{1}\) norm of coherence will not generate the same ordering for some single-qubit mixed states. Nevertheless, they may generate the same ordering if we only consider a special subset of single-qubit mixed states. Furthermore, we find that any two of these three special measures generate different ordering for single-qubit mixed states. Finally, we discuss the degree of violation of between \(l_{1}\) norm of coherence and Tsallis relative \(\alpha \)-entropies of coherence. In a sense, this degree can measure the difference between these two coherence measures in ordering states.     

Connecting unextendible maximally entangled base with partial Hadamard matrices

We study the unextendible maximally entangled bases (UMEB) in \(\mathbb {C}^{d}\bigotimes \mathbb {C}^{d}\) and connect the problem to the partial Hadamard matrices. We show that for a given special UMEB in \(\mathbb {C}^{d}\bigotimes \mathbb {C}^{d}\), there is a partial Hadamard matrix which cannot be extended to a Hadamard matrix in \(\mathbb {C}^{d}\). As a corollary, any \((d-1)\times d\) partial Hadamard matrix can be extended to a Hadamard matrix, which answers a conjecture about \(d=5\). We obtain that for any d there is a UMEB except for \(d=p\ \text {or}\ 2p\), where \(p\equiv 3\mod 4\) and p is a prime. The existence of different kinds of constructions of UMEBs in \(\mathbb {C}^{nd}\bigotimes \mathbb {C}^{nd}\) for any \(n\in \mathbb {N}\) and \(d=3\times 5 \times 7\) is also discussed.     

Quantum codes from cyclic codes over $$F_q+uF_q+vF_q+uvF_q$$

In this paper, we study quantum codes over \(F_q\) from cyclic codes over \(F_q+uF_q+vF_q+uvF_q,\) where \(u^2=u,~v^2=v,~uv=vu,~q=p^m\), and p is an odd prime. We give the structure of cyclic codes over \(F_q+uF_q+vF_q+uvF_q\) and obtain self-orthogonal codes over \(F_q\) as Gray images of linear and cyclic codes over \(F_q+uF_q+vF_q+uvF_q\). In particular, we decompose a cyclic code over \(F_q+uF_q+vF_q+uvF_q\) into four cyclic codes over \(F_q\) to determine the parameters of the corresponding quantum code.     

Throughput maximization for speed scaling with agreeable deadlines

We study the following energy-efficient scheduling problem. We are given a set of n jobs which have to be scheduled by a single processor whose speed can be varied dynamically. Each job \(J_j\) is characterized by a processing requirement (work) \(p_j\), a release date \(r_j\), and a deadline \(d_j\). We are also given a budget of energy E which must not be exceeded and our objective is to maximize the throughput (i.e., the number of jobs which are completed on time). We show that the problem can be solved optimally via dynamic programming in \(O(n^4 \log n \log P)\) time when all jobs have the same release date, where P is the sum of the processing requirements of the jobs. For the more general case with agreeable deadlines where the jobs can be ordered so that, for every \(i < j\), it holds that \(r_i \le r_j\) and \(d_i \le d_j\), we propose an optimal dynamic programming algorithm which runs in \(O(n^6 \log n \log P)\) time. In addition, we consider the weighted case where every job \(J_j\) is also associated with a weight \(w_j\) and we are interested in maximizing the weighted throughput (i.e., the total weight of the jobs which are completed on time). For this case, we show that the problem becomes \(\mathcal{NP}\)-hard in the ordinary sense even when all jobs have the same release date and we propose a pseudo-polynomial time algorithm for agreeable instances.     

Counter machines and crystallographic structures

One way to depict a crystallographic structure is by a periodic (di)graph, i.e., a graph whose group of automorphisms has a translational subgroup of finite index acting freely on the structure. We establish a relationship between periodic graphs representing crystallographic structures and an infinite hierarchy of intersection languages \(\mathcal {DCL}_d,\,d=0,1,2,\ldots \), within the intersection classes of deterministic context-free languages. We introduce a class of counter machines that accept these languages, where the machines with d counters recognize the class \(\mathcal {DCL}_d\). An intersection of d languages in \(\mathcal {DCL}_1\) defines \(\mathcal {DCL}_d\). We prove that there is a one-to-one correspondence between sets of walks starting and ending in the same unit of a d-dimensional periodic (di)graph and the class of languages in \(\mathcal {DCL}_d\). The proof uses the following result: given a digraph \(\Delta \) and a group G, there is a unique digraph \(\Gamma \) such that \(G\le \mathrm{Aut}\,\Gamma ,\,G\) acts freely on the structure, and \(\Gamma /G \cong \Delta \).     

Good and asymptotically good quantum codes derived from algebraic geometry

In this paper, we construct several new families of quantum codes with good parameters. These new quantum codes are derived from (classical) t-point (\(t\ge 1\)) algebraic geometry (AG) codes by applying the Calderbank–Shor–Steane (CSS) construction. More precisely, we construct two classical AG codes \(C_1\) and \(C_2\) such that \(C_1\subset C_2\), applying after the well-known CSS construction to \(C_1\) and \(C_2\). Many of these new codes have large minimum distances when compared with their code lengths as well as they also have small Singleton defects. As an example, we construct a family \({[[46, 2(t_2 - t_1), d]]}_{25}\) of quantum codes, where \(t_1 , t_2\) are positive integers such that \(1<t_1< t_2 < 23\) and \(d\ge \min \{ 46 - 2t_2 , 2t_1 - 2 \}\), of length \(n=46\), with minimum distance in the range \(2\le d\le 20\), having Singleton defect at most four. Additionally, by applying the CSS construction to sequences of t-point (classical) AG codes constructed in this paper, we generate sequences of asymptotically good quantum codes.     

Monogamy and polygamy for multi-qubit W-class states using convex-roof extended negativity of assistance and Rényi-$$\alpha $$ entropy

We present some new analytical polygamy inequalities satisfied by the x-th power of convex-roof extended negativity of assistance with \(x\ge 2\) and \(x\le 0\) for multi-qubit generalized W-class states. Using Rényi-\(\alpha \) entropy (R\(\alpha \)E) with \(\alpha \in [(\sqrt{7}-1)/2, (\sqrt{13}-1)/2]\), we prove new monogamy and polygamy relations. We further show that the monogamy inequality also holds for the \(\mu \)th power of Rényi-\(\alpha \) entanglement. Moreover, we study two examples in multipartite higher-dimensional system for those new inequalities.     

Exact and approximate flexible aggregate similarity search

Aggregate similarity search, also known as aggregate nearest-neighbor (Ann) query, finds many useful applications in spatial and multimedia databases. Given a group Q of M query objects, it retrieves from a database the objects most similar to Q, where the similarity is an aggregation (e.g., \({{\mathrm{sum}}}\), \(\max \)) of the distances between each retrieved object p and all the objects in Q. In this paper, we propose an added flexibility to the query definition, where the similarity is an aggregation over the distances between p and any subset of \(\phi M\) objects in Q for some support \(0< \phi \le 1\). We call this new definition flexible aggregate similarity search and accordingly refer to a query as a flexible aggregate nearest-neighbor ( Fann ) query. We present algorithms for answering Fann queries exactly and approximately. Our approximation algorithms are especially appealing, which are simple, highly efficient, and work well in both low and high dimensions. They also return near-optimal answers with guaranteed constant-factor approximations in any dimensions. Extensive experiments on large real and synthetic datasets from 2 to 74 dimensions have demonstrated their superior efficiency and high quality.     

Flexible bandwidth assignment with application to optical networks

We introduce two scheduling problems, the flexible bandwidth allocation problem (\(\textsc {FBAP}\)) and the flexible storage allocation problem (\(\textsc {FSAP}\)). In both problems, we have an available resource, and a set of requests, each consists of a minimum and a maximum resource requirement, for the duration of its execution, as well as a profit accrued per allocated unit of the resource. In \(\textsc {FBAP}\), the goal is to assign the available resource to a feasible subset of requests, such that the total profit is maximized, while in \(\textsc {FSAP}\) we also require that each satisfied request is given a contiguous portion of the resource. Our problems generalize the classic bandwidth allocation problem (BAP) and storage allocation problem (SAP) and are therefore \(\text {NP-hard}\). Our main results are a 3-approximation algorithm for \(\textsc {FBAP}\) and a \((3+\epsilon )\)-approximation algorithm for \(\textsc {FSAP}\), for any fixed \(\epsilon >0 \). These algorithms make nonstandard use of the local ratio technique. Furthermore, we present a \((2+\epsilon )\)-approximation algorithm for \(\textsc {SAP}\), for any fixed \(\epsilon >0 \), thus improving the best known ratio of \(\frac{2e-1}{e-1} + \epsilon \). Our study is motivated also by critical resource allocation problems arising in all-optical networks.