A Complete Characterization of the Gap between Convexity and SOS-Convexity

Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials, via the definition of convexity, its first order characterization, and its second order characterization, are equivalent. These three equivalent algebraic conditions, henceforth referred to as sos-convexity, can be checked by semidefinite programming whereas deciding convexity is NP-hard. If we denote the set of convex and sos-convex polynomials in $n$ variables of degree $d$ with $\tilde{C}_{n,d}$ and $\tilde{\Sigma C}_{n,d}$ respectively, then our main contribution is to prove that $\tilde{C}_{n,d}=\tilde{\Sigma C}_{n,d}$ if and only if $n=1$ or $d=2$ or $(n,d)=(2,4)$. We also present a complete characterization for forms (homogeneous polynomials) except for the case $(n,d)=(3,4)$ which is joint work with G. Blekherman and is to be published elsewhere. Our result states that the set $C_{n,d}$ of convex forms in $n$ variables of degree $d$ equals the set $\Sigma C_{n,d}$ of sos-convex forms if and only if $n=2$ or $d=2$ or $(n,d)=(3,4)$. To prove these results, we present in particular explicit examples of polynomials in $\tilde{C}_{2,6}\setminus\tilde{\Sigma C}_{2,6}$ and $\tilde{C}_{3,4}\setminus\tilde{\Sigma C}_{3,4}$ and forms in $C_{3,6}\setminus\Sigma C_{3,6}$ and $C_{4,4}\setminus\Sigma C_{4,4}$, and a general procedure for constructing forms in $C_{n,d+2}\setminus\Sigma C_{n,d+2}$ from nonnegative but not sos forms in $n$ variables and degree $d$. Although for disparate reasons, the remarkable outcome is that convex polynomials (resp. forms) are sos-convex exactly in cases where nonnegative polynomials (resp. forms) are sums of squares, as characterized by Hilbert.Comment: 25 pages; minor editorial revisions made; formal certificates for computer assisted proofs of the paper added to arXi

Cosmological constant influence on cosmic string spacetime

We investigate the line element of spacetime around a linear cosmic string in the presence of a cosmological constant. We obtain the metric and argue that it should be discarded because of asymptotic considerations. Then a time dependent and consistent form of the metric is obtained and its properties are discussed.Comment: 3 page

Proving Craig and Lyndon Interpolation Using Labelled Sequent Calculi

We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents, and nested sequents. Here we adapt the method to a more general external formalism of labelled sequents and provide sufficient criteria on the Kripke-frame characterization of a logic that guarantee the IPs. In particular, we show that classes of frames definable by quantifier-free Horn formulas correspond to logics with the IPs. These criteria capture the modal cube and the infinite family of transitive Geach logics

Pemberdayaan Masyarakat Marannu melalui Pertanian dan Peternakan Terintegrasi dalam Rangka Mewujudkan Kabupaten Pinrang sebagai Poros Utama Pemenuhan Pangan Nasional

Tujuan kegiatan ini yaitu Penumbuhkan empati, jiwa kepemimpinan, kewirausahaan, kerja sama mahasiswa, dan dapat memberikan sumbangan bagi penyelesaian persoalan yang ada di masyarakat. Secara Khusus kegiatan ini bertujuan untuk meningkatkan kualitas dan kuantitas produksi pertanian dan peternakan dengan menghasilkan pakan ternak dari pengolahan limbah pertanian dan pupuk organik dari pengolahan limbah peternakan. Metode Pelaksanaan yang diterapkan untuk mencapai tujuan yaitu (1) Sosialisasi Pertanian: Penggunaan pupuk organik dan bahaya penggunaan pupuk kimia, (2) Sosialisasi Peternakan: Pemenuhan gisi dan pemberian vaksin ternak, (3) Pengolahan limbah pertanian menjadi pakan ternak, (4) Pengolahan limbah peternakan menjadi pupuk organik, dan (5) Pemberdayaan masyarakat pengangguran dalam pengolahan pupuk organik dan pakan ternak, Hasil (Luaran) dalam kegiatan ini adalah (1) Meningkatkannya hasil panen pertanian dari jumlah hasil panen sebelumnya, (2) Terjadinya penurunan biaya produksi atau pembelian pakan ternak dari periode sebelumnya dan (3) 50% petani Desa marannu menggunakan pupuk organik hasil pengolahan Limbah dan Peternakan 50% Peternak Desa Marannu menggunakan pakan ternak hasil pengolahan limbah pertanian. Konsep pertanian dan peternakan terintegrasi sebagai langkah Kabupaten Pinrang Sebagai Poros Utama Pemenuhan Pangan Nasiona

Teleparallel Energy-Momentum Distribution of Static Axially Symmetric Spacetimes

This paper is devoted to discuss the energy-momentum for static axially symmetric spacetimes in the framework of teleparallel theory of gravity. For this purpose, we use the teleparallel versions of Einstein, Landau-Lifshitz, Bergmann and M$\ddot{o}$ller prescriptions. A comparison of the results shows that the energy density is different but the momentum turns out to be constant in each prescription. This is exactly similar to the results available in literature using the framework of General Relativity. It is mentioned here that M$\ddot{o}$ller energy-momentum distribution is independent of the coupling constant $\lambda$. Finally, we calculate energy-momentum distribution for the Curzon metric, a special case of the above mentioned spacetime.Comment: 14 pages, accepted for publication in Mod. Phys. Lett.

Probing Micro-quasars with TeV Neutrinos

The jets associated with Galactic micro-quasars are believed to be ejected by accreting stellar mass black-holes or neutron stars. We show that if the energy content of the jets in the transient sources is dominated by electron-proton plasma, then a several hour outburst of 1--100 TeV neutrinos produced by photo- meson interactions should precede the radio flares associated with major ejection events. Several neutrinos may be detected during a single outburst by a 1km^2 detector, thereby providing a powerful probe of micro-quasars jet physics.Comment: Accepted to PRL. More detailed discussion of particle acceleratio

Duel and sweep algorithm for order-preserving pattern matching

Given a text $T$ and a pattern $P$ over alphabet $\Sigma$, the classic exact matching problem searches for all occurrences of pattern $P$ in text $T$. Unlike exact matching problem, order-preserving pattern matching (OPPM) considers the relative order of elements, rather than their real values. In this paper, we propose an efficient algorithm for OPPM problem using the "duel-and-sweep" paradigm. Our algorithm runs in $O(n + m\log m)$ time in general and $O(n + m)$ time under an assumption that the characters in a string can be sorted in linear time with respect to the string size. We also perform experiments and show that our algorithm is faster that KMP-based algorithm. Last, we introduce the two-dimensional order preserved pattern matching and give a duel and sweep algorithm that runs in $O(n^2)$ time for duel stage and $O(n^2 m)$ time for sweeping time with $O(m^3)$ preprocessing time.Comment: 13 pages, 5 figure

CLIMATE CHANGE IMPACT ON MOUNTAIN BIODIVERSITY: A SPECIAL REFERENCE TO GILGIT-BALTISTAN OF PAKISTAN

Climate Change is not a stationary phenomenon; it moves from time to time, it represents a major threat to mountainous biodiversity and to ecosystem integrity. The present study is an attempt to identify the current knowledge gap and the effects of climate change on mountainous biodiversity, a special reference to the Gilgit-Baltistan is briefly reviewed. Measuring the impact of climate change on mountain biodiversity is quite challenging, because climate change interacts with every phenomenon of ecosystem. The scale of this change is so large and very adverse so strongly connected to ecosystem services, and all communities who use natural resources. This study aims to provide the evidences on the basis of previous literature, in particular context to mountain biodiversity of Gilgit-Baltistan (GB). Mountains of Gilgit-Baltistan have most fragile ecosystem and are more vulnerable to climate change. These mountains host variety of wild fauna and flora, with many endangered species of the world. There are still many gaps in our knowledge of literature we studied because very little research has been conducted in Gilgit-Baltistan about climate change particular to biodiversity. Recommendations are made for increased research efforts in future this including jointly monitoring programs, climate change models and ecological research. Understanding the impact of climate change particular to biodiversity of GB is very important for sustainable management of these natural resources. The Government organizations, NGOs and the research agencies must fill the knowledge gap, so that it will help them for policy making, which will be based on scientific findings and research based

Preparation and quality control of 177Lu-[tris(1,10-phenanthroline) lutetium(III)] complex for therapy

The 177Lu-[tris(1,10-phenanthroline)lutetium(III)] complex (177Lu-PQ3) was prepared successfully with high radiochemical purity (> 99%). Lu-177 chloride was obtained by thermal neutron flux (4 × 1013 n.cm–2.s–1) of natural Lu2(NO3)3 sample, dissolved in acidic media. The radiochemical yield was checked by measuring the radiochemical purity of the 177Lu-PQ complex by ITLC (10 mM DTPA, pH = 5, as mobile phase). The final complex solution was injected intravenously into wild-type male rats and bio-distribution of the complex was checked for up to 48 hours. The dose limiting organs were shown to be the reticulu-endothelial system. The bio-distribution of the labelled compounds in tumour-bearing animals is under investigation. Nuclear Med Rev 2010; 13, 2: 49–5

Suffix Tree of Alignment: An Efficient Index for Similar Data

We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has $|A|+|B|$ leaves and can be constructed in $O(|A|+|B|)$ time. However, if the two strings are similar, the generalized suffix tree is not efficient because it does not exploit the similarity which is usually represented as an alignment of $A$ and $B$. In this paper we propose a space/time-efficient suffix tree of alignment which wisely exploits the similarity in an alignment. Our suffix tree for an alignment of $A$ and $B$ has $|A| + l_d + l_1$ leaves where $l_d$ is the sum of the lengths of all parts of $B$ different from $A$ and $l_1$ is the sum of the lengths of some common parts of $A$ and $B$. We did not compromise the pattern search to reduce the space. Our suffix tree can be searched for a pattern $P$ in $O(|P|+occ)$ time where $occ$ is the number of occurrences of $P$ in $A$ and $B$. We also present an efficient algorithm to construct the suffix tree of alignment. When the suffix tree is constructed from scratch, the algorithm requires $O(|A| + l_d + l_1 + l_2)$ time where $l_2$ is the sum of the lengths of other common substrings of $A$ and $B$. When the suffix tree of $A$ is already given, it requires $O(l_d + l_1 + l_2)$ time.Comment: 12 page