The Lattice of integer partitions and its infinite extension

In this paper, we use a simple discrete dynamical system to study the integers partitions and their lattice. The set of the reachable configurations equiped with the order induced by the transitions of the system is exactly the lattice of integer partitions equiped with the dominance ordering. We first explain how this lattice can be constructed, by showing its strong self-similarity property. Then, we define a natural extension of the system to infinity. Using a self-similar tree, we obtain an efficient coding of the obtained lattice. This approach gives an interesting recursive formula for the number of partitions of an integer, where no closed formula have ever been found. It also gives informations on special sets of partitions, such as length bounded partitions.Comment: To appear in LNCS special issue, proceedings of ORDAL'99. See http://www.liafa.jussieu.fr/~latap

Contingency designs for attitude determination of TRMM

In this paper, several attitude estimation designs are developed for the Tropical Rainfall Measurement Mission (TRMM) spacecraft. A contingency attitude determination mode is required in the event of a primary sensor failure. The final design utilizes a full sixth-order Kalman filter. However, due to initial software concerns, the need to investigate simpler designs was required. The algorithms presented in this paper can be utilized in place of a full Kalman filter, and require less computational burden. These algorithms are based on filtered deterministic approaches and simplified Kalman filter approaches. Comparative performances of all designs are shown by simulating the TRMM spacecraft in mission mode. Comparisons of the simulation results indicate that comparable accuracy with respect to a full Kalman filter design is possible

Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain

By taking the freezing limit of a spin Calogero-Sutherland model containing `anyon like' representation of the permutation algebra, we derive the exact partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain. This partition function allows us to study global properties of the spectrum like level density distribution and nearest neighbour spacing distribution. It is found that, for supersymmetric HS spin chains with large number of lattice sites, continuous part of the energy level density obeys Gaussian distribution with a high degree of accuracy. The mean value and standard deviation of such Gaussian distribution can be calculated exactly. We also conjecture that the partition function of supersymmetric HS spin chain satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom.Comment: Latex, 32 pages, 4 figures, minor typos corrected, to be published in Nucl. Phys.

Effects of local hypothermia-rewarming on physiology, metabolism and inflammation of acutely injured human spinal cord.

In five patients with acute, severe thoracic traumatic spinal cord injuries (TSCIs), American spinal injuries association Impairment Scale (AIS) grades A-C, we induced cord hypothermia (33 °C) then rewarming (37 °C). A pressure probe and a microdialysis catheter were placed intradurally at the injury site to monitor intraspinal pressure (ISP), spinal cord perfusion pressure (SCPP), tissue metabolism and inflammation. Cord hypothermia-rewarming, applied to awake patients, did not cause discomfort or neurological deterioration. Cooling did not affect cord physiology (ISP, SCPP), but markedly altered cord metabolism (increased glucose, lactate, lactate/pyruvate ratio (LPR), glutamate; decreased glycerol) and markedly reduced cord inflammation (reduced IL1β, IL8, MCP, MIP1α, MIP1β). Compared with pre-cooling baseline, rewarming was associated with significantly worse cord physiology (increased ICP, decreased SCPP), cord metabolism (increased lactate, LPR; decreased glucose, glycerol) and cord inflammation (increased IL1β, IL8, IL4, IL10, MCP, MIP1α). The study was terminated because three patients developed delayed wound infections. At 18-months, two patients improved and three stayed the same. We conclude that, after TSCI, hypothermia is potentially beneficial by reducing cord inflammation, though after rewarming these benefits are lost due to increases in cord swelling, ischemia and inflammation. We thus urge caution when using hypothermia-rewarming therapeutically in TSCI

Interpolated sequences and critical LL-values of modular forms

Recently, Zagier expressed an interpolated version of the Ap\'ery numbers for $\zeta(3)$ in terms of a critical $L$-value of a modular form of weight 4. We extend this evaluation in two directions. We first prove that interpolations of Zagier's six sporadic sequences are essentially critical $L$-values of modular forms of weight 3. We then establish an infinite family of evaluations between interpolations of leading coefficients of Brown's cellular integrals and critical $L$-values of modular forms of odd weight.Comment: 23 pages, to appear in Proceedings for the KMPB conference: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theor

Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model

By using the fact that Polychronakos-like models can be obtained through the `freezing limit' of related spin Calogero models, we calculate the exact spectrum as well as partition function of SU(m|n) supersymmetric Polychronakos (SP) model. It turns out that, similar to the non-supersymmetric case, the spectrum of SU(m|n) SP model is also equally spaced. However, the degeneracy factors of corresponding energy levels crucially depend on the values of bosonic degrees of freedom (m) and fermionic degrees of freedom (n). As a result, the partition functions of SP models are expressed through some novel q-polynomials. Finally, by interchanging the bosonic and fermionic degrees of freedom, we obtain a duality relation among the partition functions of SP models.Comment: Latex, 20 pages, no figures, minor typos correcte

Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere

We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective coordinates. Then we calculate the overlaps between these two wave functions at various fillings and small numbers of electrons. We find that the overlaps are all most equal to one. This gives a further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory and the composite fermion theory, are physically equivalent.Comment: 37 pages, revte