Duality for convex infinite optimization on linear spaces

This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A reformulation of the convex infinite optimization problem with a single constraint leads to a limiting formula for the corresponding Lagrangian dual, called sup-dual, and also for the primal problem in the case when strong Slater condition holds, which also entails strong sup-duality.This research was partially supported by Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI), and European Regional Development Fund (ERDF), Project PGC2018-097960-B-C22

Vacuum Structure and Flavor Symmetry Breaking in Supersymmetric SO(n_c) Gauge Theories

We determine the vacuum structure and phases of N=1 theories obtained via a mass \mu for the adjoint chiral superfield in N=2, SO(n_c) SQCD. For large number of flavors these theories have two groups of vacua. The first exhibits dynamical breaking of flavor symmetry \USp(2n_f) \to U(n_f) and arises as a relevant deformation of a non-trivial superconformal theory. These are in the confined phase. The second group, in an IR-free phase with unbroken flavor symmetry, is produced from a Coulomb branch singularity with Seiberg's dual gauge symmetry. In the large-\mu regime both groups of vacua are well-described by dual quarks and mesons, and dynamical symmetry breaking in the first group occurs via meson condensation. We follow the description of these vacua from weak to strong coupling and demonstrate a nontrivial agreement between the phases and the number of vacua in the two regimes. We construct the semiclassical monopole flavor multiplets and argue that their multiplicity is consistent with the number of N=1 vacua.Comment: 67 pages, harvmac; Typos corrected, section 4.1 reworde

Constraining gravitational and cosmological parameters with astrophysical data

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 189-199).We use astrophysical data to shed light on fundamental physics by constraining parametrized theoretical cosmological and gravitational models. Gravitational parameters are those constants that parametrize possible departures from Einstein's general theory of relativity (GR). We develop a general framework to describe torsion in the space time around the Earth, and show that certain observables of the Gravity Probe B (GPB) experiment can be computed in this framework. We examine a toy model showing how a specific theory in this framework can be constrained by GPB data. We also search for viable theories of gravity where the Ricci scalar R in the Lagrangian is replaced by an arbitrary function f(R). Making use of the equivalence between such theories and scalar-tensor gravity, we find that models can be made consistent with solar system constraints either by giving the scalar a high mass or by exploiting the so-called Chameleon Effect. We explore observational constraints from the late-time cosmic acceleration, big bang nucleosynthesis and inflation. Cosmology can successfully describe the evolution of our universe using six or more adjustable cosmological parameters. There is growing interest in using 3-dimensional neutral hydrogen mapping with the redshifted 21 cm line as a cosmological probe. We quantify how the precision with which cosmological parameters can be measured depends on a broad range of assumptions. We present an accurate and robust method for measuring cosmological parameters that exploits the fact that the ionization power spectra are rather smooth functions that can be accurately fit by 7 phenomenological parameters. We find that a future square kilometer array optimized for 21 cm tomography could have great potential, improving the sensitivity to spatial curvature and neutrino masses by up to two orders of magnitude, to k 0.0002 and m 0.007eV, and giving a 4s detection of the spectral index running predicted by the simplest inflation models.by Yi Mao.Ph.D

Principles, structure and application of dynamic regional sector model of Finnish agriculture

Työssä osoitetaan, että EU:n Agenda 2000-maatalousuudistusten vaikutukset ovat aiemmin laskettuja vaikutuksia suurempia. Maidon hinnan aleneminen 15 %:lla vuosina 2005-2008 alentaa tuottajien tuloja. Tämä puolestaan vähentää investointeja, hidastaa teknologista muutosta ja heikentää kilpailukykyä, mikä johtaa edelleen tuotannon ja tulojen vähenemiseen. Työssä on rakennettu Suomen maataloustuotantoa, elintarvikkeiden kulutusta ja ulkomaankauppaa kuvaava dynaaminen ja alueellinen sektorimalli maatalouspolitiikan vaikutusten tutkimiseen. Malli simuloi maataloustuotannon kehitystä annetuilla maatalouspolitiikan skenaarioilla vuoteen 2010. Maatalouden biologiset lainalaisuudet sekä investointien pitkä aikajänne, tyypillisesti 10-30 vuotta, hidastavat maatalouden sopeutumista muuttuvaan maatalouspolitiikkaan. Taloudellista tasapainoa, ts. optimaalista tuotantorakennetta, on muuttuvissa olosuhteissa vaikea saavuttaa. Oletuksena on, että maatalous sopeutuu maatalouspolitiikan, eli tuotehintojen, tukien ja tuotantokiintiöiden muutoksiin asteittain perättäisten epätasapainotilojen kautta. Maatalouden investointeja sekä taloudellisen ja teknologisen muutoksen vuorovaikutusta on mallinnettu teknologisen diffuusion käsitteeseen perustuen. Investointeja suunnittelevien viljelijöiden tieto uusista teknologisista ratkaisuista lisääntyy sitä nopeammin, mitä useampi viljelijä investoi uusiin tekniikoihin. Teknologinen muutos maataloudessa on itseään ruokkiva polkuriippuva prosessi, jota on vaikea ennustaa staattisilla malleilla.This study presents a dynamic regional sector model for Finnish agriculture (DREMFIA) to be used in evaluating the effects of different agricultural policies on production and agricultural income in Finland. Since agriculture is characterised by the long duration of investments, the economic adjustment to policy changes, like the EU integration and Agenda 2000, is likely to take a long time. Recursive programming has been used in simulating annual market reactions and economic adjustments. A process of adjustments in dis-equilibrium is assumed. The theoretical basis of the chosen modelling methodology is presented and discussed. Two versions of the model are presented. The base model assumes exogenous efficiency development, i.e. labour and capital inputs needed per hectare and animal, in agriculture. In the Finnish agriculture technical change is largely a policy variable because of the publicly financed and controlled investment aid system. Using the base model one may analyse the levels of production and income at different levels of efficiency development. The technology diffusion model used in the extended version models the change in capital invested in alternative production techniques. The change in capital is affected by the profitability of each technique, as well as the relative spread of each technique, i.e. commonly used techniques are more accessible to farmers. Hence, the new best performing techniques may only gradually replace the existing ones. In both variants, empirically validated production functions are used in determining the milk yields of dairy cows and crop yields. Feed use of animals is endogenous in the model, as is the number of animals and hectares of crops. Appropriate energy, protein, and roughage requirements of animals are included. Agricultural policy measures are modelled in detail in all 14 production regions in the model. Processing activities of 18 different dairy products have been included. Domestic and imported products are assumed imperfect substitutes (Armington assumption). It is found that Agenda 2000 results in larger grain areas and farm income in medium term, but in lower milk and beef production volumes in the long term compared to the base scenario. Also farm income will slightly decrease due to the Agenda 2000 dairy reform starting at 2005. It is also found that the long term effects of Agenda 2000 on milk production are larger if the endogenous investments are taken into account in the analysis. IvokMTT Taloustutkimus (MTTL). Yksikön huom.: mk