A survey of indian logic from the point of view of computer science

Indian logic has a long history. It somewhat covers the domains of two of the six schools (darsanas) of Indian philosophy, namely, Nyaya and Vaisesika. The generally accepted definition of Indian logic over the ages is the science which ascertains valid knowledge either by means of six senses or by means of the five members of the syllogism. In other words, perception and inference constitute the subject matter of logic. The science of logic evolved in India through three ages: the ancient, the medieval and the modern, spanning almost thirty centuries. Advances in Computer Science, in particular, in Artificial Intelligence have got researchers in these areas interested in the basic problems of language, logic and cognition in the past three decades. In the 1980s, Artificial Intelligence has evolved into knowledge-based and intelligent system design, and the knowledge base and inference engine have become standard subsystems of an intelligent system. One of the important issues in the design of such systems is knowledge acquisition from humans who are experts in a branch of learning (such as medicine or law) and transferring that knowledge to a computing system. The second important issue in such systems is the validation of the knowledge base of the system i.e. ensuring that the knowledge is complete and consistent. It is in this context that comparative study of Indian logic with recent theories of logic, language and knowledge engineering will help the computer scientist understand the deeper implications of the terms and concepts he is currently using and attempting to develop.

Bipartite Powers of k-chordal Graphs

Let k be an integer and k >= 3. A graph G is k-chordal if G does not have an induced cycle of length greater than k. From the definition it is clear that 3-chordal graphs are precisely the class of chordal graphs. Duchet proved that, for every positive integer m, if G m is chordal then so is G(m+2). Brandst `` adt et al. in Andreas Brandsadt, Van Bang Le, and Thomas Szymczak. Duchet- type theorems for powers of HHD- free graphs. Discrete Mathematics, 177(1- 3): 9- 16, 1997.] showed that if G m is k - chordal, then so is G(m+2). Powering a bipartite graph does not preserve its bipartitedness. In order to preserve the bipartitedness of a bipartite graph while powering Chandran et al. introduced the notion of bipartite powering. This notion was introduced to aid their study of boxicity of chordal bipartite graphs. The m - th bipartite power G(m]) of a bipartite graph G is the bipartite graph obtained from G by adding edges (u; v) where d G (u; v) is odd and less than or equal to m. Note that G(m]) = G(m+1]) for each odd m. In this paper we show that, given a bipartite graph G, if G is k-chordal then so is G m], where k, m are positive integers with k >= 4

On Additive Combinatorics of Permutations of Z(n)

Let Z(n) denote the ring of integers modulo n. A permutation of Z(n) is a sequence of n distinct elements of Z(n). Addition and subtraction of two permutations is defined element-wise. In this paper we consider two extremal problems on permutations of Z(n), namely, the maximum size of a collection of permutations such that the sum of any two distinct permutations in the collection is again a permutation, and the maximum size of a collection of permutations such that no sum of two distinct permutations in the collection is a permutation. Let the sizes be denoted by s (n) and t (n) respectively. The case when n is even is trivial in both the cases, with s (n) = 1 and t (n) = n!. For n odd, we prove (n phi(n))/2(k) <= s(n) <= n!.2(-)(n-1)/2/((n-1)/2)! and 2 (n-1)/2 . (n-1/2)! <= t (n) <= 2(k) . (n-1)!/phi(n), where k is the number of distinct prime divisors of n and phi is the Euler's totient function.

Two player game variant of the Erdos-Szekeres problem

The classical Erdos-Szekeres theorem states that a convex k-gon exists in every sufficiently large point set. This problem has been well studied and finding tight asymptotic bounds is considered a challenging open problem. Several variants of the Erdos-Szekeres problem have been posed and studied in the last two decades. The well studied variants include the empty convex k-gon problem, convex k-gon with specified number of interior points and the chromatic variant. In this paper, we introduce the following two player game variant of the Erdos-Szekeres problem: Consider a two player game where each player playing in alternate turns, place points in the plane. The objective of the game is to avoid the formation of the convex k-gon among the placed points. The game ends when a convex k-gon is formed and the player who placed the last point loses the game. In our paper we show a winning strategy for the player who plays second in the convex 5-gon game and the empty convex 5-gon game by considering convex layer configurations at each step. We prove that the game always ends in the 9th step by showing that the game reaches a specific set of configurations.

Identification of a discrete intermediate in the assembly disassembly of physalis mottle tymovirus through mutational analysis

Assembly intermediates of icosahedral viruses are usually transient and are difficult to identify. In the present investigation, site-specific and deletion mutants of the coat protein gene of physalis mottle tymovirus (PhMV) were used to delineate the role of specific amino acid residues in the assembly of the virus and to identify intermediates in this process. N-terminal 30, 34, 35 and 39 amino acid deletion and single C-terminal (N188) deletion mutant proteins of PhMV were expressed in Escherichia coli. Site-specific mutants H69A, C75A, W96A, D144N, D144N-T151A, K143E and N188A were also constructed and expressed. The mutant protein lacking 30 amino acid residues from the N terminus self-assembled to T = 3 particles in vivo while deletions of 34, 35 and 39 amino acid residues resulted in the mutant proteins that were insoluble. Interestingly, the coat protein (pR PhCP) expressed using pRSET B vector with an additional 41 amino acid residues at the N terminus also assembled into T = 3 particles that were more compact and had a smaller diameter. These results demonstrate that the amino-terminal segment is flexible and either the deletion or addition of amino acid residues at the N terminus does not affect T = 3 capsid assembly, in contrast, the deletion of even a single residue from the C terminus (PhN188 Delta 1) resulted in capsids that were unstable. These capsids disassembled to a discrete intermediate with a sedimentation coefficent of 19.4 S. However, the replacement of C-terminal asparagine 188 by alanine led to the formation of stable capsids. The C75A and D144N mutant proteins also assembled into capsids that were as stable as the pR PhCP, suggesting that C75A and D144 are not crucial for the T = 3 capsid assembly. pR PhW96A and pR PhD144N-T151A mutant proteins failed to form capsids and were present as heterogeneous aggregates. Interestingly, the pR PhK143E mutant protein behaved in a manner similar to the C-terminal deletion protein in forming unstable capsids. The intermediate with an s value of 19.4 S was the major assembly product of pR PhH69A mutant protein and could correspond to a 30mer. It is possible that the assembly or disassembly is arrested at a similar stage in pR PhN188 Delta 1, pR PhH69A and pR PhK143E mutant proteins.

Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

Applying pure mathematics: mathematics in the natural sciences

The book of nature is written in the language of mathematics. This quotation, attributed to Galileo, seemed to hold to an unreasonable1 extent in the era of quantum mechanics.

Approximation algorithm for maximum independent set in planar traingle-free graphs

The maximum independent set problem is NP-complete even when restricted to planar graphs, cubic planar graphs or triangle free graphs. The problem of finding an absolute approximation still remains NP-complete. Various polynomial time approximation algorithms, that guarantee a fixed worst case ratio between the independent set size obtained to the maximum independent set size, in planar graphs have been proposed. We present in this paper a simple and efficient, O(|V|) algorithm that guarantees a ratio 1/2, for planar triangle free graphs. The algorithm differs completely from other approaches, in that, it collects groups of independent vertices at a time. Certain bounds we obtain in this paper relate to some interesting questions in the theory of extremal graphs.

Correlation, Coding, and Cooperation in Wireless Sensor Networks

We consider a single-hop data-gathering sensor network, consisting of a set of sensor nodes that transmit data periodically to a base-station. We are interested in maximizing the lifetime of this network. With our definition of network lifetime and the assumption that the radio transmission energy consumption forms the most significant portion of the total energy consumption at a sensor node, we attempt to enhance the network lifetime by reducing the transmission energy budget of sensor nodes by exploiting three system-level opportunities. We pose the problem of maximizing lifetime as a max-min optimization problem subject to the constraint of successful data collection and limited energy supply at each node. This turns out to be an extremely difficult optimization to solve. To reduce the complexity of this problem, we allow the sensor nodes and the base-station to interactively communicate with each other and employ instantaneous decoding at the base-station. The chief contribution of the paper is to show that the computational complexity of our problem is determined by the complex interplay of various system-level opportunities and challenges.

Weak consistency of read-only transactions: A tool to improve concurrency in heterogeneous locking protocols

Three different types of consistencies, viz., semiweak, weak, and strong, of a read-only transaction in a schedule s of a set T of transactions are defined and these are compared with the existing notions of consistencies of a read-only transaction in a schedule. We present a technique that enables a user to control the consistency of a read-only transaction in heterogeneous locking protocols. Since the weak consistency of a read-only transaction improves concurrency in heterogeneous locking protocols, the users can help to improve concurrency in heterogeneous locking protocols by supplying the consistency requirements of read-only transactions. A heterogeneous locking protocol P' derived from a locking protocol P that uses exclusive mode locks only and ensures serializability need not be deadlock-free. We present a sufficient condition that ensures the deadlock-freeness of Pprime, when P is deadlock-free and all the read-only transactions in Pprime are two phase.

Applications of reverse saturable absorbers in laser science

A variety of applications exist for reverse saturable absorbers (RSAs) in the area of optical pulse processing and computing. An RSA can be used as power limiter/pulse smoother and energy limiter/pulse shortner of laser pulses. A combination of RSA and saturable absorber (SA) can be used for mode locking and pulse shaping between high power laser amplifiers in oscillator amplifier chain. Also, an RSA can be used for the construction of a molecular spatial light modulator (SLM) which acts as an input/output device in optical computers. A detailed review of the theoretical studies of these processes is presented. Current efforts to find RSAs at desired wavelength for testing these theoretical predictions are also discussed.

Rudiments of complexity theory for scientists and engineers

Complexity theory is an important and growing area in computer science that has caught the imagination of many researchers in mathematics, physics and biology. In order to reach out to a large section of scientists and engineers, the paper introduces elementary concepts in complexity theory in a informal manner, motivating the reader with many examples.

Dynamic path profile aided recompilation in a JAVA just-in-time compiler

Just-in-Time (JIT) compilers for Java can be augmented by making use of runtime profile information to produce better quality code and hence achieve higher performance. In a JIT compilation environment, the profile information obtained can be readily exploited in the same run to aid recompilation and optimization of frequently executed (hot) methods. This paper discusses a low overhead path profiling scheme for dynamically profiling AT produced native code. The profile information is used in recompilation during a subsequent invocation of the hot method. During recompilation tree regions along the hot paths are enlarged and instruction scheduling at the superblock level is performed. We have used the open source LaTTe AT compiler framework for our implementation. Our results on a SPARC platform for SPEC JVM98 benchmarks indicate that (i) there is a significant reduction in the number of tree regions along the hot paths, and (ii) profile aided recompilation in LaTTe achieves performance comparable to that of adaptive LaTTe in spite of retranslation and profiling overheads.