Computationally Efficient Modeling and Data Assimilation of Near-Surface Variability

Near-surface (< 20m) ocean exhibits high variability due to coupled interactions, for e.g., with the atmosphere, sea ice, land, etc. Here we focus on atmospheric heat and momentum (wind) forcing, which are known to cause diurnal variability within the mixed layer. Only recently with a combination of sufficiently high vertical/horizontal resolution (75L, 1/4deg) and sub-daily atmospheric forcing fields, ocean models are starting to resolve this diurnal variability. However, the computation expense of such a high vertical resolution is burdensome in the context of coupled modeling and data assimilation. An alternative approach is to parameterize this diurnal variability with a prognostic model, that is embedded into the ocean model.In the first part of this presentation, we will demonstrate results with the above two approaches, by comparing them to profiles of near-surface temperature and salinity. In the context of data assimilation and reanalysis, this modeling capability opens the door to re-examine and perhaps improve specification of background (or, ensemble) error characteristics. The second half of this talk will focus on illustrating diurnally varying errors within an ensemble DA, and possible approaches to improve localization (horizontal/vertical) to extract maximum possible observational information content from in-situ and satellite observations of sea surface temperature

Adoption of Indigenous Dairy Management Practices among Tribal Farm Women

The study was conducted among the tribal farm women of West Garo Hills District of Meghalaya, India with the objective to determine the extent of adoption of indigenous dairy management practices. Proportionate random sampling was used in selection of 120 respondents. Practices having rationality for adoption of indigenous dairy management practices were collected and the data were analyzed using percentage analysis. The findings revealed that majority of the respondents adopted care and management of dry and pregnant cows. This was followed by adoption of other practices viz.., selection of breed and feeding, care during and after calving and milking technique

Eigenvector Procedure based on Weighted Preference Flows in Multicriteria Outranking Analysis

The outranking analysis has been frequently used to deal with the complex decisions involving qualitative criteria and imprecise data. So far, various versions of ELECTRE have been proposed for ranking alternatives in the outranking analysis. Among others, ELECTRE III has been widely used. A distillation procedure using a qualification index is proposed to rank alternatives from the valued outranking relation. A weakness of ELECTRE III, however, is to involve the arbitrariness in the selection of the discrimination threshold function for the distillation procedure. On the other hand, various variants of PROMETHEE are also proposed for the outranking analysis. PROMETHEE intends to be simple and easy to understand. A deficiency of PROMETHEE is that it does not take into account the preference intensity of alternatives in the in-preference flow and out-preference flow for each alternative. We propose a new preference ranking procedure based on eigenvector using the gweightedh in- and outpreference flows of each alternative in the outranking analysis. The basic idea of the procedure proposed here is that it should be better to outrank a gstrongh alternative than a gweakh one and, conversely, it is less serious to be outranked by a gstrongh alternative than by gweakh one in a PROMETHEE context. It has a completely different interpretation with the AHP (Analytic Hierarchy Process) since the components of the valued outranking relation matrix are neither ratios nor reciprocal as in the AHP.Multiple criteria analysis; PROMETHEE; ELECTRE; Valued outranking relations

Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem

In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups, finding hidden subgroups of groups with small commutator subgroup and of groups admitting an elementary Abelian normal 2-subgroup of small index or with cyclic factor group.Comment: 10 page

Quantum Algorithms for the Triangle Problem

We present two new quantum algorithms that either find a triangle (a copy of $K_{3}$) in an undirected graph $G$ on $n$ nodes, or reject if $G$ is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes $\tilde{O}(n^{10/7})$ queries. The second algorithm uses $\tilde{O}(n^{13/10})$ queries, and it is based on a design concept of Ambainis~\cite{amb04} that incorporates the benefits of quantum walks into Grover search~\cite{gro96}. The first algorithm uses only $O(\log n)$ qubits in its quantum subroutines, whereas the second one uses O(n) qubits. The Triangle Problem was first treated in~\cite{bdhhmsw01}, where an algorithm with $O(n+\sqrt{nm})$ query complexity was presented, where $m$ is the number of edges of $G$.Comment: Several typos are fixed, and full proofs are included. Full version of the paper accepted to SODA'0

Separating decision tree complexity from subcube partition complexity

The subcube partition model of computation is at least as powerful as decision trees but no separation between these models was known. We show that there exists a function whose deterministic subcube partition complexity is asymptotically smaller than its randomized decision tree complexity, resolving an open problem of Friedgut, Kahn, and Wigderson (2002). Our lower bound is based on the information-theoretic techniques first introduced to lower bound the randomized decision tree complexity of the recursive majority function. We also show that the public-coin partition bound, the best known lower bound method for randomized decision tree complexity subsuming other general techniques such as block sensitivity, approximate degree, randomized certificate complexity, and the classical adversary bound, also lower bounds randomized subcube partition complexity. This shows that all these lower bound techniques cannot prove optimal lower bounds for randomized decision tree complexity, which answers an open question of Jain and Klauck (2010) and Jain, Lee, and Vishnoi (2014).Comment: 16 pages, 1 figur

Search via Quantum Walk

We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the Markov chain. The main new idea is to apply quantum phase estimation to the quantum walk in order to implement an approximate reflection operator. This operator is then used in an amplitude amplification scheme. As a result we considerably expand the scope of the previous approaches of Ambainis (2004) and Szegedy (2004). Our algorithm combines the benefits of these approaches in terms of being able to find marked elements, incurring the smaller cost of the two, and being applicable to a larger class of Markov chains. In addition, it is conceptually simple and avoids some technical difficulties in the previous analyses of several algorithms based on quantum walk.Comment: 21 pages. Various modifications and improvements, especially in Section

Linear time algorithm for quantum 2SAT

A canonical result about satisfiability theory is that the 2-SAT problem can be solved in linear time, despite the NP-hardness of the 3-SAT problem. In the quantum 2-SAT problem, we are given a family of 2-qubit projectors $\Pi_{ij}$ on a system of $n$ qubits, and the task is to decide whether the Hamiltonian $H=\sum \Pi_{ij}$ has a 0-eigenvalue, or it is larger than $1/n^\alpha$ for some $\alpha=O(1)$. The problem is not only a natural extension of the classical 2-SAT problem to the quantum case, but is also equivalent to the problem of finding the ground state of 2-local frustration-free Hamiltonians of spin $\frac{1}{2}$, a well-studied model believed to capture certain key properties in modern condensed matter physics. While Bravyi has shown that the quantum 2-SAT problem has a classical polynomial-time algorithm, the running time of his algorithm is $O(n^4)$. In this paper we give a classical algorithm with linear running time in the number of local projectors, therefore achieving the best possible complexity.Comment: 20 page

Quantum walk based search algorithms

In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum analogues of classical search procedures. We present a rather detailed description of a somewhat simplified version of the MNRS algorithm. Finally, in the query complexity model, we show how quantum walks can be applied to the following search problems: Element Distinctness, Matrix Product Verification, Restricted Range Associativity, Triangle, and Group Commutativity.Comment: 16 pages, survey pape