Kalman Filter Algorithm for Rating and Prediction in Basketball

The Thesis presents a state-space model for a basketball league and a Kalman filter algorithm for the estimation of the state of the league. In the state-space model, each of the basketball teams is associated with a rating that represents its strength compared to the other teams. The ratings are assumed to evolve in time following a stochastic process with independent Gaussian increments. The estimation of the team ratings is based on the observed game scores that are assumed to depend linearly on the true strengths of the teams and independent Gaussian noise. The team ratings are estimated using a recursive Kalman filter algorithm that produces least squares optimal estimates for the team strengths and predictions for the scores of the future games. Additionally, if the Gaussianity assumption holds, the predictions given by the Kalman filter maximize the likelihood of the observed scores. The team ratings allow probabilistic inference about the ranking of the teams and their relative strengths as well as about the teams’ winning probabilities in future games. The predictions about the winners of the games are correct 65-70% of the time. The team ratings explain 16% of the random variation observed in the game scores. Furthermore, the winning probabilities given by the model are concurrent with the observed scores. The state-space model includes four independent parameters that involve the variances of noise terms and the home court advantage observed in the scores. The Thesis presents the estimation of these parameters using the maximum likelihood method as well as using other techniques. The Thesis also gives various example analyses related to the American professional basketball league, i.e., National Basketball Association (NBA), and regular seasons played in year 2005 through 2010. Additionally, the season 2009-2010 is discussed in full detail, including the playoffs.

Structure of (4-chloro-2-methylphenoxy) acetamide

C9H10ClNO2, Mol · wt = 199.69, monoclinic, C2/c, Z = 8, a = 15.782(2) Å, b = 3.958(1) Å, c = 29.448(2) Å, β = 92.08°, ν = 1838.35 Å3, ϱc = 1.443 g cm−3, ϱ0 = 1.438(2) g cm−3. The structure of (4-chloro-2-methylphenoxy) acetamide (2M4ClPA) was determined by direct methods and refined by full-matrix least-squares methods to R = 0.079. The molecules dimerize about a centre of symmetry and the N – H⋯O distance is = 2.909(3) Å.

Crystal structure of the charge-transfer complex promethazine picrate

Promethazine picrate (C23H23N5O7S) crystallises in the triclinic space group P[unk] with a = 8.137(1), b = 8.144(3), c = 19.224(6) Å, α = 87.78(3), β = 79.97(2), γ = 70.57(2)° and two molecules per unit cell. The structure was solved by direct methods (MULTAN 80) using 2438 observed reflections [I > 2.5 σ(I)]. Refinement was carried out by block-diagonal least-squares methods to a final R = 0.052. The picrate group is planar and is almost perpendicular to the promethazine plane. The two groups are joined by a hydrogen bond. The pairs of molecules related by a centre of symmetry make a molecular arrangement where promethazine and picrate groups are packed in sheets in three dimensions.

Crystal and molecular structure of l-valyl-l-lysine hydrochloride

l-Valyl-l-lysine hydrochloride, C11N3O3H23 HCl, rystallizes in the monoclinic space group P2, with a = 5.438(5), b = 14.188(5), c = 9.521(5) Å, β= 95.38(2)° and Z = 2. The crystal structure, solved by direct methods, refined to R = 0.036, using full matrix least-squares method. The peptide exists in a zwitterionic form, with the N atom of the lysine side-chain protonated. The two γ-carbons of the valine side-chain have positional disorder, giving rise to two conformations, χ111= -67.3 and 65.9°, one of which (65.9°) is sterically less favourable and has been found to be less popular amongst residues branching at β-C. The lysine side-chain has the geometry of g− tgt, not seen in crystal structures of the dipeptides reported so far. Interestingly, χ32 (63.6°) of lysine side-chain has a gauche+ conformation unlike in most of the other tructures, where it is trans. The neighbouring peptide molecules are hydrogen bonded in a head-to-tail fashion, a rather uncommon interaction in lysine peptide structures. The structure shows considerable similarity with that of l-Lys-l-Val HO in conformational angles and H-bond interactions [4].

Organometallic derivatives of diphosphazanes. 2. Seven-coordinated Group 6 metal tricarbonyl complexes of diphosphazane ligands. X-ray crystal structure of [WI2(CO)3{P(OPh)2}2NPh]

The reactions of the complexes [MI2(CO)3-(NCMe)2] (M = Mo, W) with the diphosphazane ligands RN{P(OPh)2}2 (R = Me, Ph) in CH2Cl2 at room temperature afford new seven-coordinated complexes of the type [MI2(CO)3{P(OPh)2}2NR]. The molybdenum complexes are sensitive to air oxidation even in the solid state, whereas the tungsten complexes are more stable in the solid state and in solution. The structure of the tungsten complex [WI2(CO)3{P(OPh)2}2NPh] has been determined by single-crystal X-ray diffraction. It crystallizes in the orthorhombic system with the space group Pna 2(1), a = 19.372 (2) angstrom, b = 11.511 (1) angstrom, c = 15.581 (1) angstrom, and Z = 4. Full-matrix least-squares refinement with 3548 reflections (I > 2.5-sigma-(I)) led to final R and R(w) values of 0.036 and 0.034, respectively. The complex adopts a slightly distorted pentagonal-bypyramidal geometry rarely observed for such a type of complexes; two phosphorus atoms of the diphosphazane ligand, two iodine atoms, and a carbonyl group occupy the equatorial plane, and the other two carbonyl groups, the apical positions.

Preparation, characterization, spectral and thermal analyses of (N2H5)2MCl4·2H2O (M = Fe, Co, Ni and Cu); crystal structure of the iron complex

Hydrazinium metal chlorides, (N2H5)2MCl4·2H2O (where M = Fe, Co, Ni and Cu), have been prepared from the aqueous solutions of the respective metal chlorides and hydrazine hydrochloride (N2H4·HCl or N2H4·2HCl) and investigated by spectral and thermal analyses. The crystal structure of the iron complex has been determined by direct methods and refined by full-matrix least-squares to an R of 0.023 and Rw of 0.031 for 1495 independent reflections. The structure shows ferrous ion in an octahedral environment bonded by two hydrazinium cations, two chloride anions and two water molecules. In the complex cation [Fe(N2H5)2(H2O)2Cl2]2+, the coordinated groups are in trans positions.

Structure of bovine prothrombin fragment 1 refined at 2.25 Å resolution

The structure of bovine prothrombin fragment 1 has been refined at 2.25 Å resolution using high resolution measurements made with the synchrotron beam at CHESS. The synchrotron data were collected photographically by oscillation methods (R-merge = 0.08). These were combined with lower order diffractometer data for refinement purposes. The structure was refined using restrained least-squares methods with the program PROLSQ to a crystallographic R-value of 0.175. The structure includes 105 water molecules with occupancies of >0·6. The first 35 residues (Ala1-Leu35) of the N-terminal ?-carboxy glutamic acid-domain (Ala1-Cys48) of fragment 1 are disordered as are two carbohydrate chains of Mr ? 5000; the latter two combine to render 40% of the structure disordered. The folding of the kringle of fragment 1 is related to the close intramolecular contact between the inner loop disulfide groups. Half of the conserved sequence of the kringle forms an inner core surrounding these disulfide groups. The remainder of the sequence conservation is associated with the many turns of the main chain. The Pro95 residue of the kringle has a cis conformation and Tyr74 is ordered in fragment 1, although nuclear magnetic resonance studies indicate that the comparable residue of plasminogen kringle 4 has two positions. Surface accessibility calculations indicate that none of the disulfide groups of fragment 1 is accessible to solvent.

Synthetic, spectroscopic, magnetic, and x-ray structural studies on a vitamin B6-amino acid Schiff base complex, aqua(5'-phosphopyridoxylidenetyrosinato)copper(II) tetrahydrate

A Schiff base metal complex, [Cu(II)(PLP-DL-tyrosinato)(H2O)].4H2O (PLP = pyridoxal phosphate), with the molecular formula CuC17O13N2H27P has been prepared and characterized by magnetic, spectral, and X-ray structural studies. The compound crystallizes in the triclinic space group P1BAR with a = 8.616 (2) angstrom, b = 11.843 (3) angstrom, c = 12.177 (3) angstrom, alpha = 103.40 (2)degrees, beta = 112.32 (2)degrees, gamma = 76.50 (1)degrees, and Z = 2. The structure was solved by the heavy-atom method and refined by least-squares techniques to a final R value of 0.057 for 3132 independent reflections. The coordination geometry around Cu(II) is distorted square pyramidal with phenolic oxygen, imino nitrogen, and carboxylate oxygen from the Schiff base ligand and water oxygen as basal donor atoms. The axial site is occupied by a phosphate oxygen from a neighboring molecule, thus resulting in a one-dimensional polymer. The structure reveals pi-pi interaction of the aromatic side chain of the amino acid with the pyridoxal pi system. A comparative study is made of this complex with similar Schiff base complexes. The variable-temperature magnetic behavior of this compound shows a weak antiferromagnetic interaction.

Crystal and Molecular Structure of N-acetyl-L-glutamine

The crystal and molecular structure of the title compound has been determined by direct methods from diffractometer data. Crystals are orthorhombic, with Z= 4 in a unit cell of dimensions : a= 13.811 (10), b= 5.095(5), c= 12.914(10)Å, space group P212121. The structure was refined by least-squares to R 3.31% for 868 observed reflections. There is significant non-planarity of the peptide group and its nitrogen atom is significantly pyramidal. There is no correlation between the double-bond character and reactivity of the C–N bond of the terminal amide group in glutamine and acetamide

Monetary policy rules and estimated reaction functions for the European Central Bank

This thesis studies the interest-rate policy of the ECB by estimating monetary policy rules using real-time data and central bank forecasts. The aim of the estimations is to try to characterize a decade of common monetary policy and to look at how different models perform at this task.The estimated rules include: contemporary Taylor rules, forward-looking Taylor rules, nonlinearrules and forecast-based rules. The nonlinear models allow for the possibility of zone-like preferences and an asymmetric response to key variables. The models therefore encompass the most popular sub-group of simple models used for policy analysis as well as the more unusual non-linear approach. In addition to the empirical work, this thesis also contains a more general discussion of monetary policy rules mostly from a New Keynesian perspective. This discussion includes an overview of some notable related studies, optimal policy, policy gradualism and several other related subjects. The regression estimations are performed with either least squares or the generalized method of moments depending on the requirements of the estimations. The estimations use data from both the Euro Area Real-Time Database and the central bank forecasts published in ECB Monthly Bulletins. These data sources represent some of the best data that is available for this kind of analysis. The main results of this thesis are that forward-looking behavior appears highly prevalent, but that standard forward-looking Taylor rules offer only ambivalent results with regard to inflation. Nonlinear models are shown to work, but on the other hand do not have a strong rationale over a simpler linear formulation. However, the forecasts appear to be highly useful in characterizing policy and may offer the most accurate depiction of a predominantly forward-looking central bank. In particular the inflation response appears much stronger while the output response becomes highly forward-looking as well.

Interactions of tris buffer with nucleotides: the crystal structure of tris(hydroxymethyl)methylammonium adenosine 5'-diphosphate dihydrate

The crystal and molecular structures of the Tris salt of adenosine 5'-diphosphate were determined from X-ray diffraction data. The crystals are monoclinic, space P21, and Z = 2 with a=9.198 (2) A, b=6.894 (1) A, c=18.440 (4) A, and beta = 92.55 (2) degrees. Intensity data were collected on an automated diffractometer. The structure was solved by the heavy-atom technique and refined by least squares to R = 0.047. The ADP molecule adopts a folded conformation. The conformation about the glycosidic bond is anti. The conformation of the ribose ring is close to a perfect C(2')-endo-C-(3')-exo puckering. The conformation about C(4')-C(5') is gauche-gauche, similar to other nucleotide structures. The pyrophosphate chain displays a nearly eclipsed geometry when viewed down the P-P vector, unlike the staggered conformation observed in crystal structures of other pyrophosphates. The less favorable eclipsed conformation probably results from the observed association of Tris molecules with the polar diphosphate chain through electrostatic interactions and hydrogen bonds. Such interactions may play an important role in Tris-buffered aqueous solutions of nucleotides and metal ions.

Adaptive optimal load balancing in a nonhomogeneous multiserver system with a central job scheduler

A model comprising several servers, each equipped with its own queue and with possibly different service speeds, is considered. Each server receives a dedicated arrival stream of jobs; there is also a stream of generic jobs that arrive to a job scheduler and can be individually allocated to any of the servers. It is shown that if the arrival streams are all Poisson and all jobs have the same exponentially distributed service requirements, the probabilistic splitting of the generic stream that minimizes the average job response time is such that it balances the server idle times in a weighted least-squares sense, where the weighting coefficients are related to the service speeds of the servers. The corresponding result holds for nonexponentially distributed service times if the service speeds are all equal. This result is used to develop adaptive quasi-static algorithms for allocating jobs in the generic arrival stream when the load parameters are unknown. The algorithms utilize server idle-time measurements which are sent periodically to the central job scheduler. A model is developed for these measurements, and the result mentioned is used to cast the problem into one of finding a projection of the root of an affine function, when only noisy values of the function can be observed

Turbulent flow computations on a hybrid cartesian point distribution using meshless solver LSFD-U

This paper may be considered as a sequel to one of our earlier works pertaining to the development of an upwind algorithm for meshless solvers. While the earlier work dealt with the development of an inviscid solution procedure, the present work focuses on its extension to viscous flows. A robust viscous discretization strategy is chosen based on positivity of a discrete Laplacian. This work projects meshless solver as a viable cartesian grid methodology. The point distribution required for the meshless solver is obtained from a hybrid cartesian gridding strategy. Particularly considering the importance of an hybrid cartesian mesh for RANS computations, the difficulties encountered in a conventional least squares based discretization strategy are highlighted. In this context, importance of discretization strategies which exploit the local structure in the grid is presented, along with a suitable point sorting strategy. Of particular interest is the proposed discretization strategies (both inviscid and viscous) within the structured grid block; a rotated update for the inviscid part and a Green-Gauss procedure based positive update for the viscous part. Both these procedures conveniently avoid the ill-conditioning associated with a conventional least squares procedure in the critical region of structured grid block. The robustness and accuracy of such a strategy is demonstrated on a number of standard test cases including a case of a multi-element airfoil. The computational efficiency of the proposed meshless solver is also demonstrated. (C) 2010 Elsevier Ltd. All rights reserved.

1, 2-Bis (diphenylphosphino) etane bridged dinuclear copper (I) complexes: Investigations of solid state and solution structures by CP/MAS31P NMR spectroscopy, X-ray crystallography, IR spectroscopy and solution 31P NMR and 63Cu NMR spectroscopy

Three different complexes of copper (I) with bridging 1, 2-bis(diphenylphosphino)ethane (dppe), namely [Cu2 (mu-dppe) (CH3CN)6] (ClO4)2 (1), [Cu2 (mu-dppe)2 (CH3 CN)2] (ClO4)2 (2), and [Cu2 (mu-dppe) (dppe)2 (CH3CN)2] (ClO4)2 (3) have been prepared. The structure of [Cu2 (mu-dppe) (dPPe)2 (CH3CH)2] (ClO4)2 has been determined by X-ray crystallography. It crystallizes in the space group PT with a=12.984(6) angstrom, b=13.180(6) angstrom, c=14.001(3) angstrom, alpha=105.23(3), beta=105.60(2), gamma=112.53 (4), V=1944 (3) angstrom3, and Z=1. The structure was refined by least-squares method with R=0.0365; R(w)=0.0451 for 6321 reflections with F0 greater-than-or-equal-to 3 sigma (F0). The CP/MAS P-31 and IR spectra of the complexes have been analysed in the light of available crystallographic data. IR spectroscopy is particularly helpful in identifying the presence of chelating dppe. P-31 chemical shifts observed in solid state are very different from those observed in solution, and change significantly with slight changes in structure. In solution, complex 1 remains undissociated but complexes 2 and 3 undergo extensive dissociation. With a combination of room temperature H-1, Cu-63, and variable temperature P-31 NMR spectra, it is possible to understand the various processes occurring in solution.

Suomalaisten yksityismetsien raakapuun tarjonta 1999-2009

Pro gradu -tutkielman tavoite on mallintaa suomalaisten yksityismetsien raakapuun tarjontaa vuosien 1999-2009 puukauppa-aineistolla. Tutkielman tulos on raakapuun kantohinnasta ja muista tarpeellisista selittävistä muuttujista riippuva tarjonnan funktio kaikille käsitellyille raakapuulajeille. Tutkielman toimeksiantaa UPM-Kymmene Oyj. Tarkoitus on, että tarjontafunktioiden ja lopputuotteidensa kysynnän tuntemuksen avulla UPM-Kymmene voi tarkastella mahdollisuuksiaan puunhankintaan tulevaisuudessa. Tutkielma esittelee suomalaisen raakapuumarkkinan erityispiirteitä, metsäekonomista teoriaa raakapuun tarjonnasta sekä aihetta koskevien aiempien empiiristen tutkimusten tuloksia. Esittelyn perusteella löydetään kysymyksenasettelun kannalta hinnan lisäksi kiinnostavimmat muuttujat tarjonnan vaihtelun selittämiseen. Osoittautuu, että vaikka kysyntäfunktion olemassaolon taloustieteellinen perusteltavuus suomalaisella raakapuumarkkinalla on kyseenalainen, ostomäärän ja hinnan samanaikainen määräytyminen aiheuttaa aineistossa riippuvuutta tarjontamallien virhetermin ja selittävänä muuttujana käytettävän kantohinnan välillä. Tutkielma jatkuu simultaanisuusharhan, instrumenttimuuttujamenetelmän ja kaksivaiheisen pienimmän neliösumman menetelmän esittelyllä seuraten Hamiltonin kirjaa 77me Serres Analysis (1994) sekä Davidsonin ja MacKinnonin kirjaa Econometric Theory and Methods (2004). Tarkentuvaa estimaattoria varten tarvitaan instrumenttimuuttujia, jotka valitaan kunkin raakapuulajin mallille erikseen. Osassa tarjontamalleista havaitaan estimolntimenetelmän kannalta olennaista muuttujien epästationaarisuutta, joka perustellaan seurauksettomaksi soveltaen johtopäätöksiä Hsiaon artikkelista Statistical Properties of the Tvvo-Stage Least Squares Estimator Under Cointegration (1997). Diagnostisen tarkastelun jälkeen mallit todetaan moitteettomiksi. Tulosten mukaan raakapuun tarjonnan hintajousto on korkeampi kuin esitellyissä aikaisemmissa empiirisissä tutkimuksissa. Lisäksi käsiteltyjen kuitupuulajien tarjontojen hintajoustot ovat tukkipuulajien joustoja korkeampia, mikä on metsänhoidollisin syin perusteltavaa. Tarjonta ei sen sijaan näytä juuri reagoineen käsitellylle aikajaksolle sattuneisiin veromuutoksiin. Osoittautuu myös, ettei tarjonta riipu voimakkaasti sijoitetun pääoman hinnasta eli korosta. Valtiotieteellisen tiedekunnan dekaani ja UPM-Kymmene sopivat vuonna 2009, että pro gradu -tutkielmasta säilytetään valtiotieteellisen tiedekunnan kirjastossa sensuroitua kappaletta, josta yksityiskohtaisimmat lopputulokset jätetään pois. Tämä tutkielman kappale on suppea, siten sivumäärältään tiivistelmäsivun tietoa lyhyempi.