Chapter III: Management of cardiovascular risk factors and medical therapy

Critical limb ischaemia (CLI) is a particularly severe manifestation of lower limb atherosclerosis posing a major threat to both limb and life of affected patients. Besides arterial revascularisation, risk-factor modification and administration of antiplatelet therapy is a major goal in the treatment of CLI patients. Key elements of cardiovascular risk management are smoking cessation and treatment of hyperlipidaemia with dietary modification or statins. Moreover, arterial hypertension and diabetes mellitus should be adequately treated. In CLI patients not suitable for arterial revascularisation or subsequent to unsuccessful revascularisation, parenteral prostanoids may be considered. CLI patients undergoing surgical revascularisation should be treated with beta blockers. At present, neither gene nor stem-cell therapy can be recommended outside clinical trials. Of note, walking exercise is contraindicated in CLI patients due to the risk of worsening pre-existing or causing new ischaemic wounds. CLI patients are oftentimes medically frail and exhibit significant comorbidities. Co-existing coronary heart and carotid as well as renal artery disease should be managed according to current guidelines. Considering the above-mentioned treatment goals, interdisciplinary treatment approaches for CLI patients are warranted. Aim of the present manuscript is to discuss currently existing evidence for both the management of cardiovascular risk factors and treatment of co-existing disease and to deduct specific treatment recommendations.

Rules and regulations of Plant Pest Control Branch and Plant Quarantine Branch. Title 7, Chapter III, of the Code of Federal Regulations.

Amendments [issued by Plant Quarantine Division or Plant Pest Control Division.] (1 v. loose-leaf)

Crystal Coulomb energies: I. Organic donor-acceptor complexes--a review. II. Classical Ewald calculations of the Coulomb binding energy of four donor-acceptor crystals and Wurster's blue perchlorate. III. A rapid-convergence quantum-mechanical formalism for crystal electronic energies

Chapter I

Theories for organic donor-acceptor (DA) complexes in solution and in the solid state are reviewed, and compared with the available experimental data. As shown by McConnell et al. (Proc. Natl. Acad. Sci. U.S., 53, 46-50 (1965)), the DA crystals fall into two classes, the holoionic class with a fully or almost fully ionic ground state, and the nonionic class with little or no ionic character. If the total lattice binding energy 2ε₁ (per DA pair) gained in ionizing a DA lattice exceeds the cost 2ε_o of ionizing each DA pair, ε₁ + ε_o less than 0, then the lattice is holoionic. The charge-transfer (CT) band in crystals and in solution can be explained, following Mulliken, by a second-order mixing of states, or by any theory that makes the CT transition strongly allowed, and yet due to a small change in the ground state of the non-interacting components D and A (or D⁺ and A^-). The magnetic properties of the DA crystals are discussed.

Chapter II

A computer program, EWALD, was written to calculate by the Ewald fast-convergence method the crystal Coulomb binding energy E_C due to classical monopole-monopole interactions for crystals of any symmetry. The precision of E_C values obtained is high: the uncertainties, estimated by the effect on E_C of changing the Ewald convergence parameter η, ranged from ± 0.00002 eV to ± 0.01 eV in the worst case. The charge distribution for organic ions was idealized as fractional point charges localized at the crystallographic atomic positions: these charges were chosen from available theoretical and experimental estimates. The uncertainty in E_C due to different charge distribution models is typically ± 0.1 eV (± 3%): thus, even the simple Hückel model can give decent results.

E_C for Wurster's Blue Perchl orate is -4.1 eV/molecule: the crystal is stable under the binding provided by direct Coulomb interactions. E_C for N-Methylphenazinium Tetracyanoquino- dimethanide is 0.1 eV: exchange Coulomb interactions, which cannot be estimated classically, must provide the necessary binding.

EWALD was also used to test the McConnell classification of DA crystals. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine: 7,7,8,8-Tetracyanoquinodimethan) E_C = -4.0 eV while 2ε_o = 4.6₅ eV: clearly, exchange forces must provide the balance. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine:para-Chloranil) E_C = -4.4 eV, while 2ε_o = 5.0 eV: again EC falls short of 2ε₁. As a Gedankenexperiment, two nonionic crystals were assumed to be ionized: for (1:1)-(Hexamethyl- benzene:para-Chloranil) E_C = -4.5 eV, 2ε_o = 6.6 eV; for (1:1)- (Napthalene:Tetracyanoethylene) E_C = -4.3 eV, 2ε_o = 6.5 eV. Thus, exchange energies in these nonionic crystals must not exceed 1 eV.

Chapter III

A rapid-convergence quantum-mechanical formalism is derived to calculate the electronic energy of an arbitrary molecular (or molecular-ion) crystal: this provides estimates of crystal binding energies which include the exchange Coulomb inter- actions. Previously obtained LCAO-MO wavefunctions for the isolated molecule(s) ("unit cell spin-orbitals") provide the starting-point. Bloch's theorem is used to construct "crystal spin-orbitals". Overlap between the unit cell orbitals localized in different unit cells is neglected, or is eliminated by Löwdin orthogonalization. Then simple formulas for the total kinetic energy Q^(XT)_λ, nuclear attraction [λ/λ]^XT, direct Coulomb [λλ/λ'λ']^XT and exchange Coulomb [λλ'/λ'λ]^XT integrals are obtained, and direct-space brute-force expansions in atomic wavefunctions are given. Fourier series are obtained for [λ/λ]^XT, [λλ/λ'λ']^XT, and [λλ/λ'λ]^XT with the help of the convolution theorem; the Fourier coefficients require the evaluation of Silverstone's two-center Fourier transform integrals. If the short-range interactions are calculated by brute-force integrations in direct space, and the long-range effects are summed in Fourier space, then rapid convergence is possible for [λ/λ]^XT, [λλ/λ'λ']^XT and [λλ'/λ'λ]^XT. This is achieved, as in the Ewald method, by modifying each atomic wavefunction by a "Gaussian convergence acceleration factor", and evaluating separately in direct and in Fourier space appropriate portions of [λ/λ]^XT, etc., where some of the portions contain the Gaussian factor.

Problem-solving courts, therapeutic jurisprudence and the constitution : if two is company, is three a crowd?

Court costs, resource-intensive trials, booming prison populations and the obduracy of recidivism rates all present as ugly excesses of the criminal law adversarial paradigm. To combat these excesses, problem-solving courts have evolved with an edict to address the underlying issues that have caused an individual to commit a crime. When a judge seeks to help a problem-solving court participant deal with issues like addiction, mental health or poverty, they are performing a very different role to that of a judicial officer in the traditional court hierarchy. They are no longer the removed, independent arbiter — a problem-solving court judge steps into the ‘arena’ with the participant and makes active use of their judicial authority to assist in rehabilitation and positive behavioural change. Problem-solving court judges employing the principles of therapeutic jurisprudence appreciate that their interaction with participants can have therapeutic and anti-therapeutic consequences. This article will consider how the deployment of therapeutic measures (albeit with good intention) can lead to the behavioural manifestation of partiality and bias on the part of problem-solving court judges. Chapter III of the Commonwealth Constitution will then be analysed to highlight why the operation and functioning of problem solving courts may be deemed unconstitutional. Part IV of this article will explain how a problem-solving court judge who is not acting impartially or independently will potentially contravene the requirements of the Constitution. It will finally be suggested that judges who possess a high level of emotional intelligence will be the most successful in administering an independent and impartial problem solving court.

Imagination and diversity in the philosophy of Hobbes

This dissertation is a study of some aspects of theoretical philosophy of the early modern thinker Thomas Hobbes (1588-1679). The focal point of the work is Hobbes s conception of imagination, which is discussed from both a systematic and a historical point of view, as well as in the light of contemporary scholarship. I argue that though there are significant similarities between the view of Hobbes and that of his predecessors, he gives a novel theory of imagination, which clarifies not only early modern discussions on human nature, knowledge, science, and literary criticism, but above all his own versatile philosophy. The prologue of the dissertation introduces methodological principles and gives critical remarks on the standard view of Hobbes. In Chapter II, I discuss the prominent theories of imagination before Hobbes and link them to his account. I argue that though Hobbes adopted the Aristotelian framework, his view is not reduced to it, as he borrows from various sources, for instance, from the Stoics and from Renaissance thought. Chapters III and IV form the psychological part of the work. In the Chapter III I argue that imagination, not sense, is central in the basic cognitive operations of the mind and that imagination has a decisive role in Hobbes s theory of motivation. The Chapter IV concentrates on various questions of Hobbes s philosophy of language. The chapter ends with a defence of a less naturalistic reading of Hobbes s theory of human nature. Chapters V and VI form the epistemological part of the work. I suggest, contrary to what has been recently claimed, that though Hobbes s ideas of good literary style do have a point of contact with his philosophy (e.g. the psychology of creative process), his ideas in the field are independent of his project of demonstrative political science. Instead I argue that the novelty of his major political work, Leviathan (1651), is based on a new theory of knowledge which he continued to develop in the post-Leviathan works. Chapter VII seeks to connect the more theoretical conclusions of Chapters V and VI to Hobbes's idea(l) of science as well as to his philosophical practice. On the basis of Hobbes s own writings as well as some historical examinations, I argue that method is not an apt way to conceptualise Hobbes s philosophical practice. Contemporary readings of Hobbes s theory of science are critically discussed and the chapter ends with an analysis of Hobbes s actual argumentation. In addition to the concluding remarks, the epilogue suggest three things: first, imagination is central when trying to understand Hobbes s versatile philosophy; second, that it is misleading to depict Hobbes as a simple materialist, mechanist, and empiricist; and, third, that in terms of imagination his influence on early modern thought has not been fully appreciated.

Conceptual and statistical modelling of environmental effects in population dynamics

Population dynamics are generally viewed as the result of intrinsic (purely density dependent) and extrinsic (environmental) processes. Both components, and potential interactions between those two, have to be modelled in order to understand and predict dynamics of natural populations; a topic that is of great importance in population management and conservation. This thesis focuses on modelling environmental effects in population dynamics and how effects of potentially relevant environmental variables can be statistically identified and quantified from time series data. Chapter I presents some useful models of multiplicative environmental effects for unstructured density dependent populations. The presented models can be written as standard multiple regression models that are easy to fit to data. Chapters II IV constitute empirical studies that statistically model environmental effects on population dynamics of several migratory bird species with different life history characteristics and migration strategies. In Chapter II, spruce cone crops are found to have a strong positive effect on the population growth of the great spotted woodpecker (Dendrocopos major), while cone crops of pine another important food resource for the species do not effectively explain population growth. The study compares rate- and ratio-dependent effects of cone availability, using state-space models that distinguish between process and observation error in the time series data. Chapter III shows how drought, in combination with settling behaviour during migration, produces asymmetric spatially synchronous patterns of population dynamics in North American ducks (genus Anas). Chapter IV investigates the dynamics of a Finnish population of skylark (Alauda arvensis), and point out effects of rainfall and habitat quality on population growth. Because the skylark time series and some of the environmental variables included show strong positive autocorrelation, the statistical significances are calculated using a Monte Carlo method, where random autocorrelated time series are generated. Chapter V is a simulation-based study, showing that ignoring observation error in analyses of population time series data can bias the estimated effects and measures of uncertainty, if the environmental variables are autocorrelated. It is concluded that the use of state-space models is an effective way to reach more accurate results. In summary, there are several biological assumptions and methodological issues that can affect the inferential outcome when estimating environmental effects from time series data, and that therefore need special attention. The functional form of the environmental effects and potential interactions between environment and population density are important to deal with. Other issues that should be considered are assumptions about density dependent regulation, modelling potential observation error, and when needed, accounting for spatial and/or temporal autocorrelation.

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

Generic differentiability of convex functions and monotone operators

The aim of this paper is to investigate to what extent the known theory of subdifferentiability and generic differentiability of convex functions defined on open sets can be carried out in the context of convex functions defined on not necessarily open sets. Among the main results obtained I would like to mention a Kenderov type theorem (the subdifferential at a generic point is contained in a sphere), a generic Gâteaux differentiability result in Banach spaces of class S and a generic Fréchet differentiability result in Asplund spaces. At least two methods can be used to prove these results: first, a direct one, and second, a more general one, based on the theory of monotone operators. Since this last theory was previously developed essentially for monotone operators defined on open sets, it was necessary to extend it to the context of monotone operators defined on a larger class of sets, our "quasi open" sets. This is done in Chapter III. As a matter of fact, most of these results have an even more general nature and have roots in the theory of minimal usco maps, as shown in Chapter II.

Reactions of platinum(II) complexes with dioxygen: progress toward alkane functionalization

Whereas stoichiometric activation of C-H bonds by complexes of transition metals is becoming increasingly common, selective functionalization of alkanes remains a formidable challenge in organometallic chemistry. The recent advances in catalytic alkane functionalization by transition-metal complexes are summarized in Chapter I.

The studies of the displacement of pentafluoropyridine in [(tmeda)Pt(CH_3)(NC_5F_5)][BAr^f_4] (1) with γ- tetrafluoropicoline, a very poor nucleophile, are reported in Chapter II. The ligand substitution occurs by a dissociative interchange mechanism. This result implies that dissociative loss of pentafluoropyridine is the rate-limiting step in the C-H activation reactions of 1.

Oxidation of dimethylplatinum(II) complexes (N-N)Pt(CH_3)_2 (N-N = tmeda(1), α-diimines) by dioxygen is described in Chapter III. Mechanistic studies suggest a two-step mechanism. First, a hydroperoxoplatinum(IV) complex is formed in a reaction between (N-N)Pt(CH_3)_2 and dioxygen. Next, the hydroperoxy complex reacts with a second equivalent of (N-N)Pt(CH_3)_2 to afford the final product, (N-N)Pt(OH)(OCH_3)(CH_3)_2. The hydroperoxy intermediate, (tmeda)Pt(OOH)(OCH_3)(CH_3)_2 (2), was isolated and characterized. The reactivity of 2 with several dime thylplatinum(II) complexes is reported.

The studies described in Chapter IV are directed toward the development of a platinum(II)-catalyzed oxidative alkane dehydrogenation. Stoichiometric conversion of alkanes (cyclohexane, ethane) to olefins (cyclohexene, ethylene) is achieved by C-H activation with [(N-N)Pt(CH_3)(CF_3CH_2OH)]BF_4 (1, N-N is N,N'-bis(3,5-di-t- butylphenyl)-1,4-diazabutadiene) which results in the formation of olefin hydride complexes. The first step in the C-H activation reaction is formation of a platinum(II) alkyl which undergoes β-hydrogen elimination to afford the olefin hydride complex. The cationic ethylplatinum(II) intermediate can be generated in situ by treating diethylplatinum(II) compounds with acids. Treatment of (phen)PtEt_2 with [H(OEt_2)_2]Bar^f_4 at low temperatures resulted in the formation of a mixture of [(phen)PtEt(OEt_2)]Bar^f_4 (8) and [(phen)Pt(C_2H_4)H] Bar^f_4 (7). The cationic olefin complexes are unreactive toward dioxygen or hydrogen peroxide. Since the success of the overall catalytic cycle depends on our ability to oxidize the olefin hydride complexes, a series of neutral olefin complexes of platinum(II) with monoanionic ligands (derivatives of pyrrole-2-carboxyaldehyde N-aryl imines) was prepared. Unfortunately, these are also stable to oxidation.

Social saliency : visual psychophysics and single-neuron recordings in humans

My thesis studies how people pay attention to other people and the environment. How does the brain figure out what is important and what are the neural mechanisms underlying attention? What is special about salient social cues compared to salient non-social cues? In Chapter I, I review social cues that attract attention, with an emphasis on the neurobiology of these social cues. I also review neurological and psychiatric links: the relationship between saliency, the amygdala and autism. The first empirical chapter then begins by noting that people constantly move in the environment. In Chapter II, I study the spatial cues that attract attention during locomotion using a cued speeded discrimination task. I found that when the motion was expansive, attention was attracted towards the singular point of the optic flow (the focus of expansion, FOE) in a sustained fashion. The more ecologically valid the motion features became (e.g., temporal expansion of each object, spatial depth structure implied by distribution of the size of the objects), the stronger the attentional effects. However, compared to inanimate objects and cues, people preferentially attend to animals and faces, a process in which the amygdala is thought to play an important role. To directly compare social cues and non-social cues in the same experiment and investigate the neural structures processing social cues, in Chapter III, I employ a change detection task and test four rare patients with bilateral amygdala lesions. All four amygdala patients showed a normal pattern of reliably faster and more accurate detection of animate stimuli, suggesting that advantageous processing of social cues can be preserved even without the amygdala, a key structure of the “social brain”. People not only attend to faces, but also pay attention to others’ facial emotions and analyze faces in great detail. Humans have a dedicated system for processing faces and the amygdala has long been associated with a key role in recognizing facial emotions. In Chapter IV, I study the neural mechanisms of emotion perception and find that single neurons in the human amygdala are selective for subjective judgment of others’ emotions. Lastly, people typically pay special attention to faces and people, but people with autism spectrum disorders (ASD) might not. To further study social attention and explore possible deficits of social attention in autism, in Chapter V, I employ a visual search task and show that people with ASD have reduced attention, especially social attention, to target-congruent objects in the search array. This deficit cannot be explained by low-level visual properties of the stimuli and is independent of the amygdala, but it is dependent on task demands. Overall, through visual psychophysics with concurrent eye-tracking, my thesis found and analyzed socially salient cues and compared social vs. non-social cues and healthy vs. clinical populations. Neural mechanisms underlying social saliency were elucidated through electrophysiology and lesion studies. I finally propose further research questions based on the findings in my thesis and introduce my follow-up studies and preliminary results beyond the scope of this thesis in the very last section, Future Directions.