Patterns Of Entries Research Articles

Typical ranks in symmetric matrix completion

We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank of a completion of a generic partially specified symmetric matrix depends only on the location of the specified entries, and not their values, if complex entries are allowed. When the entries are required to be real, this is no longer the case and the possible minimum ranks are called typical ranks . We give a combinatorial description of the patterns of specified entries of n × n symmetric matrices that have n as a typical rank. Moreover, we describe exactly when such a generic partial matrix is minimally completable to rank n . We also characterize the typical ranks for patterns of entries with low maximal typical rank.

Typical and generic ranks in matrix completion

We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study the minimal completion rank. If the entries of the matrix are complex and the known entries are chosen randomly according to a continuous distribution, then for a fixed pattern of locations of specified and unspecified entries, there is a unique minimum completion rank which occurs with probability one. We call this rank the generic completion rank. Over the real numbers there can be multiple ranks that occur with positive probability; we call them typical completion ranks. We introduce these notions formally, and provide a number of inequalities and exact results on typical and generic ranks for different families of patterns of known and unknown entries.

Installation entries and exits in the EU ETS: patterns and the delay effect of closure provisions

This paper analyses installation entries and exits in the EU ETS, over 2005–2013. Patterns of entries and exits are identified across countries, sectors, and time. The limitations of the EUTL as a data source for research purposes mean that only genuine exits (reflecting production capacity reduction), and not genuine entries (reflecting production capacity increases), can be systematically identified. Exits are found to be relatively frequent events, more so in manufacturing sectors with small average installation size. Moreover, exits were concentrated in 2007 and in 2012, the final years of Phase I and Phase II. We investigate whether the perverse incentives of closure provisions, in free allocation, explain such time pattern. A discrete-time hazard model for the exit event is estimated using a three-tier dataset combining installation-, firm-, and macro-level information. The results indicate that, most likely, closure provisions delayed installation exits, especially in Phase II.

Unique Flexibility Patterns of PDB Entries

Solid bodies obtain characteristic mass and charge distributions, principle rotational axes as well as internal symmetry axes. Internal symmetry axes are uniquely identified by Normal Mode Analysis (NMA) and are widely used in the fields of engineering and seismology to model the redistribution of modest energy influxes into non-rigid bodies. NMA of protein systems rapidly and reproduceably identify their internal flexibility characteristics. Protein systems typically consist of thousands of atoms and three times as many Cartesian degrees of freedom (dofs). These systems can equally well be characterized by their internal dofs: bond lengths, bond angles and bond rotations. Small energy perturbations like thermal baths primarily activate bond-rotations or dihedrals. Use of dihedral dofs ensures that bond lengths and bond angles remain stereochemically sound. We have shown that use of these dofs combined with distance- and atom-dependent Hookian potentials correctly reproduce theoretical dispersion spectra. Use of linearized potentials permits NMA of PDB coordinates: No initial, structure-distorting energy minimization is required. This feature permits analyses of PDB structures that differ only slightly such as (i) two isoforms of the same X-ray electron density, (ii) the same structure solved in two different crystal forms, or (iii) two evolutionary related proteins that share high structural, not sequence, homology. We examine the modal signatures of several cases and report meaningful differences. In one, glycoside hydrolase family 10 xylanases, the A and B isoforms of the same crystal place three out of 302 residues in alternate conformations. Their modal analyses reveal significant differences in their slowest modes, consistent with predictions that GH-10 members consist of two subgroups with differing mobility. In another, the modal analysis of two closely related tertiary structures with low sequence homology, lactadherin and Factor VIII glycoprotein, reveal significant differences consistent with H/D exchange data.

Topics in Well-being: Analysis of a Positive Psychology Exercise with Elementary School Children

The main purpose of this study is to examine and describe the subjects and themes in the data collected from a two-month positive psychology intervention with 3rd and 4th grade students. The activity required each of the students to begin and finish each school day by recording three positive events that happened during that day or the prior evening in a positive notebook that was provided to them, therefore increasing the frequency of positive thinking inside the classroom. The students were also encouraged to reflect on the personal significance and value of these positive incidents. A coding system was created to define topics and patterns of the entries. Results show that elementary school students consider academic and physical activities, as well as their friends, families, and teachers as being the most positive, although context may play an intervening role. Differences in the frequency and quality of the entries indicate that the success of this program is highly influenced by the teacher/administrator. This activity further demonstrates elementary school students' ability to express and reflect on their own emotions and well-being, a characteristic which could serve as a protective factor as they enter into adolescence.

Nonbonding Orbitals in Fullerenes: Nuts and Cores in Singular Polyhedral Graphs

A zero eigenvalue in the spectrum of the adjacency matrix of the graph representing an unsaturated carbon framework indicates the presence of a nonbonding pi orbital (NBO). A graph with at least one zero in the spectrum is singular; nonzero entries in the corresponding zero-eigenvalue eigenvector(s) (kernel eigenvectors) identify the core vertices. A nut graph has a single zero in its adjacency spectrum with a corresponding eigenvector for which all vertices lie in the core. Balanced and uniform trivalent (cubic) nut graphs are defined in terms of (-2, +1, +1) patterns of eigenvector entries around all vertices. In balanced nut graphs all vertices have such a pattern up to a scale factor; uniform nut graphs are balanced with scale factor one for every vertex. Nut graphs are rare among small fullerenes (41 of the 10 190 782 fullerene isomers on up to 120 vertices) but common among the small trivalent polyhedra (62 043 of the 398 383 nonbipartite polyhedra on up to 24 vertices). Two constructions are described, one that is conjectured to yield an infinite series of uniform nut fullerenes, and another that is conjectured to yield an infinite series of cubic polyhedral nut graphs. All hypothetical nut fullerenes found so far have some pentagon adjacencies: it is proved that all uniform nut fullerenes must have such adjacencies and that the NBO is totally symmetric in all balanced nut fullerenes. A single electron placed in the NBO of a uniform nut fullerene gives a spin density distribution with the smallest possible (4:1) ratio between most and least populated sites for an NBO. It is observed that, in all nut-fullerene graphs found so far, occupation of the NBO would require the fullerene to carry at least 3 negative charges, whereas in most carbon cages based on small nut cubic polyhedra, the NBO would be the highest occupied molecular orbital (HOMO) for the uncharged system.

The (weakly) sign symmetric P-matrix completion problems

In this paper it is shown that a partialsign symmetric P -matrix, whose digraph of specified entries is a symmetric n-cycle with n ≥ 6, can be completed to a sign symmetric P - matrix. The analogous completion property is also established for a partial weakly sign symmetric P -matrix and for a partialweakl y sign symmetric P0-matrix. Patterns of entries for 4 × 4 matrices are classified as to whether or not a partial (weakly) sign symmetric P - or weakly sign symmetric P0-matrix specifying the pattern must have completion to the same type of matrix. The relationship between the weakly sign symmetric P - and sign symmetric P -matrix completion problems is also examined.

Reliability of reporting self-measured blood pressure values by hypertensive patients

For self-measurement of blood pressure to be useful, patient reporting of test results must be reliable and accurate. Until now no study directly measured the accuracy and reliability of patients’ reporting of self-measured blood pressure values. Thirty hypertensive patients (69 ± 11 years) were instructed to measure blood pressure at home over 14 days with the highly accurate Omron IC monitor and to keep a record of all readings in a patient logbook. To assess the reliability of the records, patients were not informed about the memory capacity of the device. We compared automatically stored blood pressure readings with the respective logbook entries to analyze deletion (under-reporting), addition (over-reporting), and precision of reporting of test results. The prevalent pattern was under-reporting, averaging 36% ± 24% (3% to 89%), which occurred significantly more than over-reporting (9% ± 11%; 0% to 38%). The precision of reporting (identical values at corresponding times) was 76% ± 34% (0% to 100%). This observer error did not affect group comparisons of automatically stored values and logbook entries, although the estimated limits of agreement were wide. Blood pressure control, duration of hypertension, age, or previous use of self-measurement and patterns of logbook entries were not found to be predictive of the patients’ reliability. Our results demonstrate a substantial observer error in the reporting of self-measured blood pressure values. This bias may be reduced by memory-equipped blood pressure devices.

Extremal patterns of distinct entries in vectors in the range of a matrix

For an m × n matrix A over a field F we consider the following quantities: μ(A), the maximum multiplicity of a field element as a component of a nonzero vector in the range of A, and δ(A), the minimum number of distinct entries in a nonzero vector in the range of A. In terms of ramk(A), we describe the set of possible values of μand δ and discuss the possible relations between them. We also develop a general affine geometric structure in which the sets of values of μ and δ may be characterized linear algebraically.

Matrix patterns for eigenvalue—eigenvector Adjustment

An eigenvalue and an eigenvector of a matrix can be changed somewhat by changing some of the entries in the matrix. Patterns of entries in the matrix sufficient to obtain prechosen eigenvalue-eigenvector changes are described.

Some exact distance constants

We compute exact distance constants for certain patterns of matrix entries in low dimensions.

PATTERNS FROM LAND ALIENATION MAPS∗

Land entry and land patent data available in the original Land Office Tract Books and in the Numerical Index provide a seldom used datum plane for geographical investigation which is useful in developing the historical settlement geography of a region. Patterns of entries and patents in the Nebraska Sand Hills reflect restrictions imposed on man by the environment, the process of sequential settlement, abandoned geographical features, and other patterns which establish a conceptual base for further research. The maps provide insights that may be used to explain some aspect of the settlement process.