Patterns in permuted binary matrices

Reorganizing a dataset so that its hidden structure can be observed is useful in any data analysis task. For example, detecting a regularity in a dataset helps us to interpret the data, compress the data, and explain the processes behind the data. We study datasets that come in the form of binary matrices (tables with 0s and 1s). Our goal is to develop automatic methods that bring out certain patterns by permuting the rows and columns. We concentrate on the following patterns in binary matrices: consecutive-ones (C1P), simultaneous consecutive-ones (SC1P), nestedness, k-nestedness, and bandedness. These patterns reflect specific types of interplay and variation between the rows and columns, such as continuity and hierarchies. Furthermore, their combinatorial properties are interlinked, which helps us to develop the theory of binary matrices and efficient algorithms. Indeed, we can detect all these patterns in a binary matrix efficiently, that is, in polynomial time in the size of the matrix. Since real-world datasets often contain noise and errors, we rarely witness perfect patterns. Therefore we also need to assess how far an input matrix is from a pattern: we count the number of flips (from 0s to 1s or vice versa) needed to bring out the perfect pattern in the matrix. Unfortunately, for most patterns it is an NP-complete problem to find the minimum distance to a matrix that has the perfect pattern, which means that the existence of a polynomial-time algorithm is unlikely. To find patterns in datasets with noise, we need methods that are noise-tolerant and work in practical time with large datasets. The theory of binary matrices gives rise to robust heuristics that have good performance with synthetic data and discover easily interpretable structures in real-world datasets: dialectical variation in the spoken Finnish language, division of European locations by the hierarchies found in mammal occurrences, and co-occuring groups in network data. In addition to determining the distance from a dataset to a pattern, we need to determine whether the pattern is significant or a mere occurrence of a random chance. To this end, we use significance testing: we deem a dataset significant if it appears exceptional when compared to datasets generated from a certain null hypothesis. After detecting a significant pattern in a dataset, it is up to domain experts to interpret the results in the terms of the application.

The Skill of ECMWF Medium-Range Forecasts during the Year of Tropical Convection 2008

This study uses the European Centre for Medium-Range Weather Forecasts (ECMWF) model-generated high-resolution 10-day-long predictions for the Year of Tropical Convection (YOTC) 2008. Precipitation forecast skills of the model over the tropics are evaluated against the Tropical Rainfall Measuring Mission (TRMM) estimates. It has been shown that the model was able to capture the monthly to seasonal mean features of tropical convection reasonably. Northward propagation of convective bands over the Bay of Bengal was also forecasted realistically up to 5 days in advance, including the onset phase of the monsoon during the first half of June 2008. However, large errors exist in the daily datasets especially for longer lead times over smaller domains. For shorter lead times (less than 4-5 days), forecast errors are much smaller over the oceans than over land. Moreover, the rate of increase of errors with lead time is rapid over the oceans and is confined to the regions where observed precipitation shows large day-to-day variability. It has been shown that this rapid growth of errors over the oceans is related to the spatial pattern of near-surface air temperature. This is probably due to the one-way air-sea interaction in the atmosphere-only model used for forecasting. While the prescribed surface temperature over the oceans remain realistic at shorter lead times, the pattern and hence the gradient of the surface temperature is not altered with change in atmospheric parameters at longer lead times. It has also been shown that the ECMWF model had considerable difficulties in forecasting very low and very heavy intensity of precipitation over South Asia. The model has too few grids with ``zero'' precipitation and heavy (>40 mm day(-1)) precipitation. On the other hand, drizzle-like precipitation is too frequent in the model compared to that in the TRMM datasets. Further analysis shows that a major source of error in the ECMWF precipitation forecasts is the diurnal cycle over the South Asian monsoon region. The peak intensity of precipitation in the model forecasts over land (ocean) appear about 6 (9) h earlier than that in the observations. Moreover, the amplitude of the diurnal cycle is much higher in the model forecasts compared to that in the TRMM estimates. It has been seen that the phase error of the diurnal cycle increases with forecast lead time. The error in monthly mean 3-hourly precipitation forecasts is about 2-4 times of the error in the daily mean datasets. Thus, effort should be given to improve the phase and amplitude forecast of the diurnal cycle of precipitation from the model.

A regio and stereospecific radical annulation route to chiral tricyclo[4.3.1.o3,7]decane (isotwistane) system1 synthesis of (+)-10-α-Naphthyl-5-epi-Pupukean-9-one

Contrary to that of phenyl derivative 1 the radical 4 adds to radicophiles in an inter- followed by intra-molecular radical Michael addition (radical annulation), furnishing a novel route to chiral isotwistanes 5.

One pot synthesis of polycyclic oxygen aromatics. Part III mechanism of formation

Reaction of 6-Image -butyl-1-bromomethyl-2-(2-tetrahydropyranyloxy)-naphthalene2c with tetrachlorocatechol (TCC) in acetone in presence of K2CO3 gave diastereomers 6c and 7c. A mechanism (Scheme-1) invoking the base induced cleavage of the pyranyl ether 2 to 1,2-naphthoquinone-1-methide 8 as the first step has been postulated. The cleavage of the pyranyl ether linkage in 2 to give dimers 4 and 5 of 1,2-naphthoquinone-1-methide has been demonstrated with different bases. 1,2-Naphthoquinone-1-methide 8, thus generated, undergoes Michael addition with TCC followed by elimination of chloride ions to give a diketone, which further undergoes aldolisation with acetone to give diastereomers 6 and 7. Michael reaction of 8, generated Image from pyranyl ethers 2a-c, with tetrabromocatechol (TBC) under similar-reaction conditions gave the expected monobromo compounds 6h, 6i, 6k, 7n, 7n and 7q. The last step in the proposed mechanism, Image ., aldolisation has also been demonstrated using different ketonic solvents. Thus, reaction of 2a-c with TCC/TBC in diethyl ketone/methyl ethyl ketone under similar reaction conditions gave the expected compounds 6 and 7.

Synthesis Of (+/-)-2-Isopropyl-5,6-Dimethylbicyclo[3.2.1]Oct-6-En-8-One

Methanolic hydrogen chloride cyclization of the triketone 8, prepared from the Mannich base 7 and 2-methylcyclopentane-1,3-dione, gives ketones 9 and 10. NaBH4 reduction of 9 followed by Grignard reaction with CH3MgI affords the diol 12. Catalytic hydrogenation of 12 followed by PCC oxidation yields the ketoalcohol 13. Dehydration of 13 with SOCl2/pyridine results in a 1:1 mixture of the endo-14 and exo-15 olefins, separated by chromatography.

The identification of 14 alpha,17 beta-dihydroxyandrost-4-en-3-one monohydrate and 14 alpha,17 beta-dihydroxyandrosta-1,4-dien-3-one monohydrate, metabolites of androstenedione in Mucor piriformis

The microorganism Mucor piriformis transforms androst-4-ene-3,17-dione into a major and several minor metabolites. X-ray crystallographic analysis of two of these metabolites was undertaken to determine unambiguously their composition and chirality. Crystals belong to the orthorhombic space-group P2(1)2(1)2(1), with a = 7.199(4) angstrom and a = 6.023(3) angstrom, b = 11.719(3) angstrom and b = 13.455(4) angstrom, c = 20.409(3) angstrom and c = 20.702(4) angstrom for the two title compounds, respectively. The structures have been refined to final R values of 0.060 and 0.040, respectively.

On determining the elastic modulus of a cylindrical sample subjected to flexural excitation in a resonant column apparatus

For resonant column tests conducted in the flexure mode of excitation, a new methodology has been proposed to find the elastic modulus and associated axial strain of a cylindrical sample. The proposed method is an improvement over the existing one, and it does not require the assumption of either the mode shape or zero bending moment condition at the top of the sample. A stepwise procedure is given to perform the necessary calculations. From a number of resonant column experiments on aluminum bars and dry sand samples, it has been observed that the present method as compared with the one available in literature provides approximately (i) 5.9%-7.3% higher values of the elastic modulus and (ii) 6.5%-7.3% higher values of the associated axial strains.

Choosing the Arranged One, Arranging the Chosen One – Imagining an Indian Modernity: Reconciling Love, Marriage and Family On and Off the Screen

This is a study on the changing practices of kinship in Northern India. The change in kinship arrangements, and particularly in intermarriage processes, is traced by analysing the reception of Hindi popular cinema. Films and their role and meaning in people´s lives in India was the object of my research. Films also provided me with a methodology for approaching my other subject-matters: family, marriage and love. Through my discussion of cultural change, the persistence of family as a core value and locus of identity, and the movie discourses depicting this dialogue, I have looked for a possibility of compromise and reconciliation in an Indian context. As the primary form of Indian public culture, cinema has the ability to take part in discourses about Indian identity and cultural change, and alleviate the conflicts that emerge within these discourses. Hindi popular films do this, I argue, by incorporating different familiar cultural narratives in a resourceful way, thus creating something new out of the old elements. The final word, however, is the one of the spectator. The “new” must come from within the culture. The Indian modernity must be imaginable and distinctively Indian. The social imagination is not a “Wild West” where new ideas enter the void and start living a life of their own. The way the young women in Dehra Dun interpreted family dramas and romantic movies highlights the importance of family and continuity in kinship arrangements. The institution of arranged marriage has changed its appearance and gained new alternative modes such as love cum arranged marriage. It nevertheless remains arranged by the parents. In my thesis I have offered a social description of a cultural reality in which movies act as a built-in part. Movies do not work as a distinct realm, but instead intertwine with the social realities of people as a part of a continuum. The social imagination is rooted in the everyday realities of people, as are the movies, in an ontological and categorical sense. According to my research, the links between imagination and social life were not so much what Arjun Appadurai would call global and deterritorialised, but instead local and conventional.

Spin-1 Kitaev model in one dimension

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J Sigma(nSnSn+1y)-S-x. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z(2)-valued conserved quantity W-n for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2N sectors, of unequal sizes. The number of states in most of the sectors grows as d(N), where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(root 5+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground-state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term lambda Sigma W-n(n), and show that this has gapless excitations in the range lambda(c)(1)<=lambda <=lambda(c)(2). We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points lambda(c)(1) and lambda(c)(2).

A Vicarious One-Pot Transformation of a Fluorocyclitol to a Polycyclitol: Observation of a Formal 4-Fold Axial-Equatorial Epimerization on a Conformationally Locked Scaffold

A conformationally locked fluoropentol undergoes an interesting transformation to (trans,anti,trans,anti,trans)-perhydro-2,3,4a,6,7,8a-naphthalenehexol essentially under conditions of base-induced transesterification. The proposed rationale for the observed metamorphosis involves a nucleophilic displacement of fluoride, and subsequent stereo- and regioselective anti-Furst-Plattner-type ring-opening of the epoxide thus formed.

Time-Dependent Dynamics of a Planar Galaxy Model

Time-dependent models of collisionless stellar systems with harmonic potentials allowing for an essentially exact analytic description have recently been described. These include oscillating spheres and spheroids. This paper extends the analysis to time-dependent elliptic discs. Although restricted to two space dimensions, the systems are richer in that their parameters form a 10-dimensional phase space (in contrast to six for the earlier models). Apart from total energy and angular momentum, two additional conserved quantities emerge naturally. These can be chosen as the areas of extremal sections of the ellipsoidal region of phase space occupied by the system (their product gives the conserved volume). The present paper describes the construction of these models. An application to a tidal encounter is given which allows one to go beyond the impulse approximation and demonstrates the effects of rotation of the perturbed system on energy and angular-momentum transfer. The angular-momentum transfer is shown to scale inversely as the cube of the encounter velocity for an initial configuration of the perturbed galaxy with zero quadrupole moment.