Input Length Research Articles

Uniformity is Weaker than Semi-Uniformity for Some Membrane Systems

We investigate computing models that are presented as families of finite computing devices with a uniformity condition on the entire family. Examples of such models include Boolean circuits, membrane systems, DNA computers, chemical reaction networks and tile assembly systems, and there are many others. However, in such models there are actually two distinct kinds of uniformity condition. The first is the most common and well-understood, where each input length is mapped to a single computing device (e.g. a Boolean circuit) that computes on the finite set of inputs of that length. The second, called semi-uniformity, is where each input is mapped to a computing device for that input (e.g. a circuit with the input encoded as constants). The former notion is well-known and used in Boolean circuit complexity, while the latter notion is frequently found in literature on nature-inspired computation from the past 20 years or so. Are these two notions distinct? For many models it has been found that these notions are in fact the same, in the sense that the choice of uniformity or semi-uniformity leads to characterisations of the same complexity classes. In other related work, we showed that these notions are actually distinct for certain classes of Boolean circuits. Here, we give analogous results for membrane systems by showing that certain classes of uniform membrane systems are strictly weaker than the analogous semi-uniform classes. This solves a known open problem in the theory of membrane systems. We then go on to present results towards characterising the power of these semi-uniform and uniform membrane models in terms of NL and languages reducible to the unary languages in NL, respectively.

Wavelength spacing tenable capability of optical comb filter using Polarization Maintaining Fiber

Abstract: In this paper, tuneable comb filter using single-mode fiber (SMF)has been proposed and theoretically studied its capability of tuning the output spectral spacing continuously by using the birefringence property of polarization maintaining fiber (PMF).The proposed filter consists of one QWP, one HWP, one SMF and one PMF segment . Depending on the dynamic settings of wavelength of the input signal, refractive index, and length of the fiber material the comb filter offers the continuous channel spacing tunability. Obtained output spectra are quite similar as calculated from equation. Channel spacing can be tuned at any desired value with the help of this comb filter. PMF based filter is very useful for long distance transmission.

APPROXIMATING ASYMMETRIC TSP IN EXPONENTIAL TIME

Let G be a complete directed graph with n vertices and integer edge weights in range [0,M]. It is well known that an optimal Traveling Salesman Problem (TSP) in G can be solved in 2n time and space (all bounds are given within a polynomial factor of the input length, i.e., poly(n, log M)) and this is still the fastest known algorithm. If we allow a polynomial space only, then the best known algorithm has running time 4nnlog n. For TSP with bounded weights there is an algorithm with 1.657n · M running time. It is a big challenge to develop an algorithm with 2n time and polynomial space. Also, it is well-known that TSP cannot be approximated within any polynomial time computable function unless P=NP. In this short note we propose a very simple algorithm that, for any 0 < ε < 1, finds (1+ε)-approximation to asymmetric TSP in 2nε−1 time and ε−1 · poly(n, log M) space. Thereby, for any fixed ε, the algorithm needs 2n steps and polynomial space to compute (1 + ε)-approximation.

CONGESTION CONTROL IN COMPUTER NETWORKS USING A MODIFIED RED AQM ALGORITHM

Congestion control plays an important role in netwo rk resource management in very large networks with heavy traffic. Active Queue Management (AQM) algorithms are one of the approach es to resolve the congestion problems. Majority of AQM algorithms mainly focus on single queued links. The input queued swit ches are limited in throughput and output queued sw itches require a large speedup factor so our attention is directed towards Combine d Input and Output Queued (CIOQ) switches. A simple modification to the RED AQM algorithm is proposed in this paper in order to account for the presence of both input and output queues in the switch. The weighted sum of input and output queue lengths are specifically used as the congestion measure instead of just the output queue length. The average backlog in the switch is signif icantly reduced in the low speedup region by using our modified algorithm as compared to RED without this modification. Simulati ons show that the loss rate in the modified RED sli ghtly larger than that in traditional RED but the output queue length in modi fied RED is tremendously reduced. The congestion me asure which is computed using weighting factor results in reduction of the average backlog. Using our modified algorithm simul ations indicate improvement in the queue length and switch utilization.

Linear circuits, two-variable logic and weakly blocked monoids

Following recent works that connect two-variable logic to circuits and monoids, as well as recent techniques for obtaining algebraic and logical characterizations of threshold circuits, we present an algebraic and logical characterization of the language recognition power of uniform linear threshold circuits. More specifically, for numerical predicate sets P satisfying a certain closure property, we characterize the class of languages recognized by FO[<,P]-uniform linear threshold circuits as exactly those which are recognized by a particular class of two-variable formulas that use majority quantifiers and P predicates, and are exactly those which can be recognized by a particular class of weakly blocked products of typed monoids. This correspondence will hold for any numerical predicate set which is FO[<]-closed and whose predicates do not depend on the input length.

Self-Adjustable Neural Network for speech recognition

Neural networks with fixed input length are not able to train and test data with variable lengths in one network size. This issue is very crucial when the neural networks need to deal with signals of variable lengths, such as speech. Though various methods have been proposed in segmentation and feature extraction to deal with variable lengths of the data, the size of the input data to the neural networks still has to be fixed. A novel Self-Adjustable Neural Network (SANN) is presented in this paper, to enable the network to adjust itself according to different data input sizes. The proposed method is applied to the speech recognition of Malay vowels and TIMIT isolated words. SANN is benchmarked against the standard and state-of-the-art recogniser, Hidden Markov Model (HMM). The results showed that SANN was better than HMM in recognizing the Malay vowels. However, HMM outperformed SANN in recognising the TIMIT isolated words.

Derandomized Parallel Repetition Theorems for Free Games

Raz's parallel repetition theorem (SIAM J Comput 27(3):763---803, 1998) together with improvements of Holenstein (STOC, pp 411---419, 2007) shows that for any two-prover one-round game with value at most $${1- \epsilon}$$ 1 - ? (for $${\epsilon \leq 1/2}$$ ? ? 1 / 2 ), the value of the game repeated n times in parallel on independent inputs is at most $${(1- \epsilon)^{\Omega(\frac{\epsilon^2 n}{\ell})}}$$ ( 1 - ? ) ? ( ? 2 n ? ) , where ? is the answer length of the game. For free games (which are games in which the inputs to the two players are uniform and independent), the constant 2 can be replaced with 1 by a result of Barak et al. (APPROX-RANDOM, pp 352---365, 2009). Consequently, $${n=O(\frac{t \ell}{\epsilon})}$$ n = O ( t ? ? ) repetitions suffice to reduce the value of a free game from $${1- \epsilon}$$ 1 - ? to $${(1- \epsilon)^t}$$ ( 1 - ? ) t , and denoting the input length of the game by m, it follows that $${nm=O(\frac{t \ell m}{\epsilon})}$$ n m = O ( t ? m ? ) random bits can be used to prepare n independent inputs for the parallel repetition game. In this paper, we prove a derandomized version of the parallel repetition theorem for free games and show that O(t(m + ?)) random bits can be used to generate correlated inputs, such that the value of the parallel repetition game on these inputs has the same behavior. That is, it is possible to reduce the value from $${1- \epsilon}$$ 1 - ? to $${(1- \epsilon)^t}$$ ( 1 - ? ) t while only multiplying the randomness complexity by O(t) when m = O(?). Our technique uses strong extractors to a lemma of Raz and can be also used to derandomize a parallel repetition theorem of Parnafes et al. (STOC, pp 363---372, 1997) for communication games in the special case that the game is free.

Directional Hearing by Linear Summation of Binaural Inputs at the Medial Superior Olive

Neurons in the medial superior olive (MSO) enable sound localization by their remarkable sensitivity to submillisecond interaural time differences (ITDs). Each MSO neuron has its own "best ITD" to which it responds optimally. A difference in physical path length of the excitatory inputs from both ears cannot fully account for the ITD tuning of MSO neurons. As a result, it is still debated how these inputs interact and whether the segregation of inputs to opposite dendrites, well-timed synaptic inhibition, or asymmetries in synaptic potentials or cellular morphology further optimize coincidence detection or ITD tuning. Using in vivo whole-cell and juxtacellular recordings, we show here that ITD tuning of MSO neurons is determined by the timing of their excitatory inputs. The inputs from both ears sum linearly, whereas spike probability depends nonlinearly on the size of synaptic inputs. This simple coincidence detection scheme thus makes accurate sound localization possible.

Two-Way Automata Versus Logarithmic Space

We strengthen a previously known connection between the size complexity of two-way finite automata ([InlineEquation not available: see fulltext.]) and the space complexity of Turing machines (tms). Specifically, we prove that Here, [InlineEquation not available: see fulltext.] and [InlineEquation not available: see fulltext.] are the deterministic and nondeterministic [InlineEquation not available: see fulltext.], NL and L/poly are the standard classes of languages recognizable in logarithmic space by nondeterministic tms and by deterministic tms with access to polynomially long advice, and NLL and LL/polylog are the corresponding complexity classes for space O(loglogn) and advice length poly(logn). Our arguments strengthen and extend an old theorem by Berman and Lingas and can be used to obtain variants of the above statements for other modes of computation or other combinations of bounds for the input length, the space usage, and the length of advice.

Robust Multi-Property Combiners for Hash Functions

A robust combiner for hash functions takes two candidate implementations and constructs a hash function which is secure as long as at least one of the candidates is secure. So far, hash function combiners only aim at preserving a single property such as collision-resistance or pseudorandomness. However, when hash functions are used in protocols like TLS they are often required to provide several properties simultaneously. We therefore put forward the notion of robust multi-property combiners and elaborate on different definitions for such combiners. We then propose a combiner that provably preserves (target) collision-resistance, pseudorandomness, and being a secure message authentication code. This combiner satisfies the strongest notion we propose, which requires that the combined function satisfies every security property which is satisfied by at least one of the underlying hash function. If the underlying hash functions have output length n, the combiner has output length 2n. This basically matches a known lower bound for black-box combiners for collision-resistance only, thus the other properties can be achieved without penalizing the length of the hash values. We then propose a combiner which also preserves the property of being indifferentiable from a random oracle, slightly increasing the output length to 2n+?(logn). Moreover, we show how to augment our constructions in order to make them also robust for the one-wayness property, but in this case require an a priory upper bound on the input length.

On consistent inconsistencies

The most common measure for an algorithm's efficiency is its running time, described as a function of the input length. Traditionally, however, several inconsistencies have found their way even to the analysis of the most classical algorithms. In some cases these are 'slight' inconsistencies, in the sense that their effect may change the result by a factor of lgn. Some others have a polynomial effect, and on the extreme---an exponential one. We discuss this matter, bringing pairs of examples for each of the categories of effect. In the first member of the pair, the algorithm's running time is calculated accurately, whereas in the other member, it is analyzed incorrectly, demonstrating that the computing community is being inconsistent when it comes to algorithm analysis. The article's intention is not to ask authors of textbooks on algorithms to produce modified editions of their books. Rather, it wishes to raise the question of inconsistency in our treatment of algorithm analysis among various algorithms.

Tolerance Ring Design in the Actuator Arm of a Hard Disk Drive Using Finite Element Analysis

This paper presents conceptual designs for the tolerance ring in the Hard Disk Drive (HDD) in order to reduce the total deformation of the tolerance ring and decrease the installation force during the assembly process of the actuator arm, while maintaining the natural frequency within the specification range. In this research, finite element analysis was employed to compare and analyze the installation forces, total deformations of the tolerance ring and the natural frequencies of Actuator Pivot Flex Assembly (APFA). Around its cylindrical body, the tolerance ring consists of several waves which provide rigidity for the APFA assembly to resist the axial rocking motion of the actuator arm. The idea is to decrease the contact surface area between the waves and the e-block by smoothing the contact surface of the waves along the installation direction while maintaining sufficient friction to resist the axial rocking motion. The objective of this research was to minimize the total deformation and installation force. The three input variables, i.e. width, length and height of the alternating flat curve design, were analyzed together by using the engineering optimization. The decreasing of the total deformation of the tolerance ring and installation force during APFA assembly would increase the number of cycles of the reworking process which can help increase the productivity and efficiency of HDD manufacturing.

Security of Hash-then-CBC Key Wrapping Revisited

Key wrapping schemes are used to encrypt data of high entropy, such as cryptographic keys. There are two known security definitions for key wrapping schemes. One captures the security against chosen plaintext attacks (called DAE-security), and the other captures known plaintext attacks (called AKW-security). In this paper, we revisit the security of Hash-then-CBC key wrapping schemes. At SKEW 2011, Osaki and Iwata showed that the U CC -then-CBC key wrapping scheme, a key wrapping scheme that uses the U CC hash function and the CBC mode, has provable AKW-security. In this paper, we show that the scheme achieves the stronger notion of DAE-security. We also show our proof in the variable input length setting, where the adversary is allowed making queries of varying lengths. To handle such a setting, we generalize the previous definition of the U CC hash function to the variable input length setting, and show an efficient construction that meets the definition. We next consider linear-then-CBC, 2nd-preimage-resistant-then-CBC, and universal-then-CBC schemes. At SAC 2009, Gennaro and Halevi noted that these schemes do not achieve DAE-security. However, details were not presented, and we show concrete and efficient chosen plaintext attacks on these schemes, and confirm that they do not achieve DAE-security.

일라이어스와 페레즈의 방식에 기반한 하이브리드 무작위화 함수

본 논문에서는 점근적으로 최적인 두가지의 무작위화 함수인 일라이어스(Elias) 함수와 페레즈(Peres) 함수의 장단점을 고려한 하이브리드 무작위화 함수를 제안한다. 무작위화 함수는 편향성이 있는 무작위수의 공급원으로부터 균등한 무작위수를 생성하는데 쓰이는 알고리즘을 수학적으로 추상화한 것이다. 일라이어스 함수와 페레즈 함수는 입력의 길이가 무한으로 증가함에 따라 그 출력효율성이 정보론적 한계치에 다가간다. 특히, 일라이어스 함수는 주어진 (유한의) 입력길이에 대해 최적인 무작위화 함수이다. 그러나 그 계산은 간단하지 않고, 주어진 입력길이에 의존한다. 반면, 페레즈 함수는 정해진 입력의 길이에 대해 출력효율이 최적이지는 않으나, 점근적으로는 최적이고, 간단한 재귀식에 의해 정의되어서 그 계산이 매우 간단하고 적은 메모리를 필요로 한다. 이러한 계산복잡도와 출력효율에 대한 두가지 무작위화 함수의 장단점에 주목하여, 각각의 장점을 고려한 하이브리드 무작위화 함수를 제안하고 이를 분석한다. Proposed is a hybrid randomizing function using two asymptotically optimal randomizing functions: Elias function and Peres function. Randomizing function is an mathematical abstraction of producing a uniform random bits from a source of randomness with bias. It is known that the output rate of Elias function and Peres function approaches to the information-theoretic upper bound. Especially, for each fixed input length, Elias function is optimal. However, its computation is relatively complicated and depends on input lengths. On the contrary, Peres function is defined by a simple recursion. So its computation is much simpler, uniform over the input lengths, and runs on a small footprint. In view of this tradeoff between computational complexity and output efficiency, we propose a hybrid randomizing function that has strengths of the two randomizing functions and analyze it.

A Spheroid Weighted‐Axis Converter of Vestibular Schwannoma Size

To evaluate spheroid models of vestibular schwannoma (VS) size for bidirectional conversion of maximum diameter in the cistern and 3-dimensional volume. Methodological study. Academic tertiary referral center. Magnetic resonance imaging studies from 91 patients with VS from 2003 to 2011 were analyzed. Linear measurements defining meatal and cisternal components were extracted. Geometrically based conformal models of tumor volume were compared with measured tumor volume using a semiautomated computerized tracing method. Models were inverted to predict maximum axial cisternal length at the level of the internal auditory canal (IAC). A spheroid-weighted axis converter (SWC) of VS size was identified by minimizing input measurement parameters while maximizing output prediction performance. Computation steps of tumor volumes were (1) meatal-measure tumor lengths along the IAC and at the porus acusticus and take the average of a cone and cylinder and (2) cisternal-measure maximum tumor length in the axial IAC plane, use the median major:minor axis ratio of 1.26:1 to estimate minor axis length, take the geometric mean of axial dimensions to estimate axis length in the coronal plane, and apply input lengths to a spheroid. Performance error of this SWC had interquartile ranges of 33% for volume and 2 to 3 mm for maximum cisternal length. Reporting variability of VS tumor size has made it difficult to reconcile outcomes studies. We propose an accessible tool for bidirectional conversion of volumetric and linear indices of tumor size to unlock potential for meta-analyses of disparate data sets.

AN EFFICIENT PROTOCOL FOR THE QUANTUM PRIVATE COMPARISON OF EQUALITY WITH A FOUR-QUBIT CLUSTER STATE

In this paper, we further research the quantum private comparison protocol with the semi-honest participant, in which two parties can test the equality of their information without revealing the content to anyone. Considering both the success of protocol and the security of information, we first give a reasonable and significant description about the semi-honest model in quantum secure communications. Moreover, based on the feature of four-qubit cluster state which has the great robust against decoherence, we propose a new protocol for the quantum private comparison. Our protocol ingeniously utilizes the special symmetry of the four-qubit cluster state to enhance the efficiency of comparison. This new protocol is secure. The participants only know the result of comparison; cannot know each other's private information. TP cannot learn anything about the private information, even about the comparison result and the length of secret inputs.

Approximation of Boolean functions to Schaefer’s classes

We consider an algorithm for transferring Boolean functions to function classes for which the generalized satisfiability problem is solvable in polynomial time (Schaefer’s classes). For the case where an initial function is represented as a truth-table, it is proved that the complexity of the algorithm is \( {l^2} + l\,\log_2^2(l) \), where l is the input length.

Exponential size neighborhoods for makespan minimization scheduling

We investigate the quality of local search heuristics for the scheduling problem of minimizing the makespan on identical parallel machines. We study exponential size neighborhoods (whose size grows exponentially with the input length) that can be searched in polynomial time, and we derive worst-case approximation guarantees for the local optima of such neighborhoods. The so-called split neighborhood splits a feasible schedule into two layers, and then recombines the two layers by finding a perfect matching. We show that the makespan of every local optimum for split is at most a factor of 2 away from the globally optimal makespan. We then combine the split neighborhood with two neighborhoods from the literature. The combination of split with the jump neighborhood only marginally improves the approximation guarantee, whereas the combination with the lexicographic-jump neighborhood decreases the approximation guarantee from 2 to 3/2. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

A Protocol for the Quantum Private Comparison of Equality with χ-Type State

We present a new quantum protocol for comparing the equal information with the help of a semi-honest third party (TP). Different from previous protocols, we utilize the four-particle χ-type states as the information carriers. Various kinds of outside attacks and participant attacks are discussed in detail. One party cannot learn the other’s private information. The TP cannot learn any information about the private information, even about the comparison result or the length of secret inputs.

An MCMC Approach to Universal Lossy Compression of Analog Sources

Motivated by the Markov chain Monte Carlo (MCMC) approach to the compression of discrete sources developed by Jalali and Weissman, we propose a lossy compression algorithm for analog sources that relies on a finite reproduction alphabet, which grows with the input length. The algorithm achieves, in an appropriate asymptotic sense, the optimum Shannon theoretic tradeoff between rate and distortion, universally for stationary ergodic continuous amplitude sources. We further propose an MCMC-based algorithm that resorts to a reduced reproduction alphabet when such reduction does not prevent achieving the Shannon limit. The latter algorithm is advantageous due to its reduced complexity and improved rates of convergence when employed on sources with a finite and small optimum reproduction alphabet.