A Short Conceptual Proof of Narayana's Path-Counting Formula

The combinatorics of certain tuples of osculating lattice paths is studied, and a relationship with oscillating tableaux is obtained. The paths being considered have fixed start and end points on respectively the lower and right boundaries of a rectangle in the square lattice, each path can take only unit steps rightwards or upwards, and two different paths within a tuple are permitted to share lattice points, but not to cross or share lattice edges. Such path tuples correspond to configurations of the six-vertex model of statistical mechanics with appropriate boundary conditions, and they include cases which correspond to alternating sign matrices. Of primary interest here are path tuples with a fixed number $l$ of vacancies and osculations, where vacancies or osculations are points of the rectangle through which respectively no or two paths pass. It is shown that there exist natural bijections which map each such path tuple $P$ to a pair $(t,\eta)$, where $\eta$ is an oscillating tableau of length $l$ (i.e., a sequence of $l+1$ partitions, starting with the empty partition, in which the Young diagrams of successive partitions differ by a single square), and $t$ is a certain, compatible sequence of $l$ weakly increasing positive integers. Furthermore, each vacancy or osculation of $P$ corresponds to a partition in $\eta$ whose Young diagram is obtained from that of its predecessor by respectively the addition or deletion of a square. These bijections lead to enumeration formulae for tuples of osculating paths involving sums over oscillating tableaux.

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EFFICIENT COMPUTATION OF KINSHIP AND IDENTITY COEFFICIENTS ON LARGE PEDIGREES

Journal of Bioinformatics and Computational Biology ◽

10.1142/s0219720009004175 ◽

2009 ◽

Vol 07 (03) ◽

pp. 429-453 ◽

Cited By ~ 4

Author(s):

EN CHENG ◽

BRENDAN ELLIOTT ◽

Z. MERAL ÖZSOYOǦLU

Keyword(s):

Genetic Counseling ◽

Recursive Algorithm ◽

Inbreeding Coefficient ◽

Efficient Computation ◽

Counting Method ◽

Pedigree Data ◽

Encoding Scheme ◽

Kinship Coefficients ◽

Counting Formula ◽

Path Counting

With the rapidly expanding field of medical genetics and genetic counseling, genealogy information is becoming increasingly abundant. An important computation on pedigree data is the calculation of identity coefficients, which provide a complete description of the degree of relatedness of a pair of individuals. The areas of application of identity coefficients are numerous and diverse, from genetic counseling to disease tracking, and thus, the computation of identity coefficients merits special attention. However, the computation of identity coefficients is not done directly, but rather as the final step after computing a set of generalized kinship coefficients. In this paper, we first propose a novel Path-Counting Formula for calculating generalized kinship coefficients, which is motivated by Wright's path-counting method for computing inbreeding coefficient. We then present an efficient and scalable scheme for calculating generalized kinship coefficients on large pedigrees using NodeCodes, a special encoding scheme for expediting the evaluation of queries on pedigree graph structures. Furthermore, we propose an improved scheme using Family NodeCodes for the computation of generalized kinship coefficients, which is motivated by the significant improvement of using Family NodeCodes for inbreeding coefficient over the use of NodeCodes. We also perform experiments for evaluating the efficiency of our method, and compare it with the performance of the traditional recursive algorithm for three individuals. Experimental results demonstrate that the resulting scheme is more scalable and efficient than the traditional recursive methods for computing generalized kinship coefficients.

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A CONCEPTUAL PROOF OF A BASIC RESULT IN THE COMBINATORIAL APPROACH TO FREENESS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025700000157 ◽

2000 ◽

Vol 03 (02) ◽

pp. 213-222 ◽

Cited By ~ 7

Author(s):

ROLAND SPEICHER

Keyword(s):

Basic Result ◽

Direct Consequence ◽

Combinatorial Approach ◽

Free Cumulants ◽

Conceptual Proof ◽

Möbius Inversion

We present a conceptual proof for the theorem describing free cumulants with products as arguments. We reduce that theorem to a statement about the behavior of Möbius inversion under the embedding of lattices. As direct consequence of this insight we get generalizations of the theorem to the operator-valued case as well as analogous statements for classical and Boolean cumulants.

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Electron Diffraction Analysis of Microtwin Structures in Regrown (III) Silicon

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100054765 ◽

1982 ◽

Vol 40 ◽

pp. 460-461

Author(s):

P. Ling ◽

R. Gronsky ◽

J. Washburn

Keyword(s):

Electron Diffraction ◽

Ion Implantation ◽

Diffraction Analysis ◽

Diffraction Pattern ◽

Direct Consequence ◽

The Other ◽

Electron Diffraction Analysis ◽

Defect Microstructures ◽

Ion Implanted

The defect microstructures of Si arising from ion implantation and subsequent regrowth for a (111) substrate have been found to be dominated by microtwins. Figure 1(a) is a typical diffraction pattern of annealed ion-implanted (111) Si showing two groups of extra diffraction spots; one at positions (m, n integers), the other at adjacent positions between <000> and <220>. The object of the present paper is to show that these extra reflections are a direct consequence of the microtwins in the material.

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Audiology Service Models in a Family Physician Practice Setting

Perspectives on Audiology ◽

10.1044/poa6.1.24 ◽

2010 ◽

Vol 6 (1) ◽

pp. 24-32 ◽

Cited By ~ 2

Author(s):

Sridhar Krishnamurti

Keyword(s):

Pediatric Patients ◽

Practice Patterns ◽

Healthcare Delivery ◽

Direct Consequence ◽

Direct Access ◽

Practice Setting ◽

Pediatric Populations ◽

Family Practice Physicians ◽

Primary Focus ◽

Balance Problems

This article illustrates the potential of placing audiology services in a family physician’s practice setting to increase referrals of geriatric and pediatric patients to audiologists. The primary focus of family practice physicians is the diagnosis/intervention of critical systemic disorders (e.g., cardiovascular disease, diabetes, cancer). Hence concurrent hearing/balance disorders are likely to be overshadowed in such patients. If audiologists get referrals from these physicians and have direct access to diagnose and manage concurrent hearing/balance problems in these patients, successful audiology practice patterns will emerge, and there will be increased visibility and profitability of audiological services. As a direct consequence, audiological services will move into the mainstream of healthcare delivery, and the profession of audiology will move further towards its goals of early detection and intervention for hearing and balance problems in geriatric and pediatric populations.

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THE EFFECT OF GONADECTOMY ON THE RESPONSE OF THE PITUITARY I. C. S. H.-CONTENT TO STEROID SEX HORMONES

Acta Endocrinologica ◽

10.1530/acta.0.xxxv0245 ◽

1960 ◽

Vol XXXV (II) ◽

pp. 245-252 ◽

Cited By ~ 1

Author(s):

G. P. van Rees ◽

F. J. A. Paesi

Keyword(s):

Sex Hormones ◽

Sex Steroids ◽

Low Dose ◽

Testosterone Propionate ◽

Preceding Paper ◽

Direct Consequence ◽

Two Factors ◽

Reflex Stimulation ◽

Steroid Sex Hormones ◽

Stimulation Of

ABSTRACT In the experiments reported in this paper the hypothesis that the decrease in the pituitary I. C. S. H.-content, which occurs after administration of steroid sex hormones in gonadectomized animals, is counteracted by a reflex stimulation of the hypophysis initiated by the operation has been investigated. If treatment with a low dose of testosterone propionate (100 μg) was started immediately after castration, the resulting decrease in the pituitary I. C. S. H.-content became more marked if the reflex stimulation of the hypophysis had been prevented. If, however, two months were allowed to elapse before the beginning of treatment, the presence or absence of this reflex was no longer of importance for the effect of testosterone propionate on the pituitary I. C. S. H.-content. And yet, in this case too, the decrease in the pituitary I. C. S. H.-content by testosterone propionate was less than in intact animals (see preceding paper). Hence this decrease appears to be counteracted by two factors: one rapidly occurring and short lasting, resulting from a reflex elicited by gonadectomy; the other gradually increasing in potency and possibly a direct consequence of the continued absence of pituitary inhibiting sex steroids.

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Scanning-tunneling spectroscopy on conjugated polymer films

MRS Proceedings ◽

10.1557/proc-771-l4.3 ◽

2003 ◽

Vol 771 ◽

Author(s):

M. Kemerink ◽

S.F. Alvarado ◽

P.M. Koenraad ◽

R.A.J. Janssen ◽

H.W.M. Salemink ◽

...

Keyword(s):

Polymer Films ◽

Conjugated Polymer ◽

Three Dimensional ◽

Field Enhancement ◽

Direct Consequence ◽

Scanning Tunneling Spectroscopy ◽

Tunneling Spectroscopy ◽

Band Alignment ◽

Scanning Tunneling ◽

Order Of Magnitude

AbstractScanning-tunneling spectroscopy experiments have been performed on conjugated polymer films and have been compared to a three-dimensional numerical model for charge injection and transport. It is found that field enhancement near the tip apex leads to significant changes in the injected current, which can amount to more than an order of magnitude, and can even change the polarity of the dominant charge carrier. As a direct consequence, the single-particle band gap and band alignment of the organic material can be directly obtained from tip height-voltage (z-V) curves, provided that the tip has a sufficiently sharp apex.

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Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

Industrial laboratory Diagnostics of materials ◽

10.26896/1028-6861-2020-86-5-65-72 ◽

2020 ◽

Vol 86 (5) ◽

pp. 65-72

Author(s):

Yu. D. Grigoriev

Keyword(s):

Optimal Design ◽

Polynomial Regression ◽

Direct Consequence ◽

Experimental Designs ◽

Optimal Designs ◽

Software Systems ◽

General Character ◽

Support Points ◽

Optimal Weights ◽

Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

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Contemporary Developments Relating to the Inviolability of Mission Premises

10.1093/oso/9780198795940.003.0011 ◽

2017 ◽

Author(s):

Juan E Falconi Puig

Keyword(s):

Human Rights ◽

United Kingdom ◽

Urban Planning ◽

National Security ◽

Direct Consequence ◽

Access To Justice ◽

Controversial Issues ◽

The United Kingdom ◽

Domestic Legislation

This chapter addresses some of the controversial issues relating to the inviolability of mission premises. The Yvonne Fletcher incident of 1984 led to debates about the need to upgrade or reform the VCDR in that regard; and the United Kingdom, as a direct consequence of the incident, adopted the ‘Diplomatic and Consular Premises Act 1987’ to be able to adopt unilateral measures to remove premises immunity where threats to national security, to public integrity and/or the need of urban planning exist. Domestic legislation of this kind, however, also provides ground for conflicts with the VCDR. This chapter explores conflicts between property immunity and issues such as access to justice, human rights, and terrorism and examines ways of overcoming such difficulties through mechanisms which safeguard diplomatic privileges and immunity to allow the pursuit of diplomatic functions.

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