Dimension Four Wins the Same Game as the Standard Model Group

In a previous article Don Bennett and I looked for,found and proposed a game in which the Standard Model group S(U(2)XU(3)) gets singled out as the "winner". Here I propose to extend this "game" to construct a corresponding game between different potential dimensions for space time. The idea is to formulate how the same competition as the one between the potential gauge groups would run out, if restricted to the potential Lorentz or Poincare groups achievable for different dimensions of space time d. The remarkable point is that it is the experimental dimension of space time 4 which wins. So the same function defined over Lie groups seems to single out both the gauge group and the space time dimension in nature. This seems a rather strange coincidence unless there is really some similar physics behind.Comment: After introducing some more review o the previous article the historical stuff was moved into an appendi

Elements of F-ast Proton Decay

Gauge coupling unification in the Minimal Supersymmetric Standard Model (MSSM) strongly suggests the existence of a Grand Unified Theory (GUT), which could be probed by the observation of proton decay. Proton lifetime in the p \to (e+|mu+) pi0 dimension six mode is proportional in the fourth power to the GUT mass scale, and inversely proportional in the fourth power to the GUT coupling. We provide an updated dictionary of solutions for the relevant unification parameters with generic beta-function coefficients, significantly upgrading the level of detail with which second order effects are treated, and correcting subtle published errors. F-lipped SU(5) with strict MSSM field content is known to survive existing null detection limits for proton decay approaching 10^34 years, and indeed, the lifetime predicted by prior studies can be so long that successful detection is not currently plausible. Recently studied classes of F-theory derived GUT models postulate additional vector-like multiplets at the TeV scale which modify the renormalization group to yield a substantial increase in the SU(3)_C X SU(2)_L unified coupling. We find the conjunction of these models with the F-resh analysis employed to be comparatively F-ast proton decay, only narrowly evading existing detection limits, and likely falling within the observable range of proposed next generation detectors such as DUSEL and Hyper-Kamiokande. The TeV-scale vector multiplets are themselves suitable for cross correlation by the Large Hadron Collider. Their presence moreover magnifies the gap between the dual mass scales of Flipped SU(5), allowing for an elongated second stage renormalization, pushing grand unification to the doorstep of the reduced Planck mass.Comment: V2, As published in Nuclear Physics B; 57 pages, 7 figures, 12 table

Mixing multi-core CPUs and GPUs for scientific simulation software

Recent technological and economic developments have led to widespread availability of multi-core CPUs and specialist accelerator processors such as graphical processing units (GPUs). The accelerated computational performance possible from these devices can be very high for some applications paradigms. Software languages and systems such as NVIDIA's CUDA and Khronos consortium's open compute language (OpenCL) support a number of individual parallel application programming paradigms. To scale up the performance of some complex systems simulations, a hybrid of multi-core CPUs for coarse-grained parallelism and very many core GPUs for data parallelism is necessary. We describe our use of hybrid applica- tions using threading approaches and multi-core CPUs to control independent GPU devices. We present speed-up data and discuss multi-threading software issues for the applications level programmer and o er some suggested areas for language development and integration between coarse-grained and ne-grained multi-thread systems. We discuss results from three common simulation algorithmic areas including: partial di erential equations; graph cluster metric calculations and random number generation. We report on programming experiences and selected performance for these algorithms on: single and multiple GPUs; multi-core CPUs; a CellBE; and using OpenCL. We discuss programmer usability issues and the outlook and trends in multi-core programming for scienti c applications developers

The Intermediate Scale MSSM, the Higgs Mass and F-theory Unification

Even if SUSY is not present at the Electro-Weak scale, string theory suggests its presence at some scale M_{SS} below the string scale M_s to guarantee the absence of tachyons. We explore the possible value of M_{SS} consistent with gauge coupling unification and known sources of SUSY breaking in string theory. Within F-theory SU(5) unification these two requirements fix M_{SS} ~ 5 x 10^{10} GeV at an intermediate scale and a unification scale M_c ~ 3 x 10^{14} GeV. As a direct consequence one also predicts the vanishing of the quartic Higgs SM self-coupling at M_{SS} ~10^{11} GeV. This is tantalizingly consistent with recent LHC hints of a Higgs mass in the region 124-126 GeV. With such a low unification scale M_c ~ 3 x 10^{14} GeV one may worry about too fast proton decay via dimension 6 operators. However in the F-theory GUT context SU(5) is broken to the SM via hypercharge flux. We show that this hypercharge flux deforms the SM fermion wave functions leading to a suppression, avoiding in this way the strong experimental proton decay constraints. In these constructions there is generically an axion with a scale of size f_a ~ M_c/(4\pi)^2 ~ 10^{12} GeV which could solve the strong CP problem and provide for the observed dark matter. The prize to pay for these attractive features is to assume that the hierarchy problem is solved due to anthropic selection in a string landscape.Comment: 48 pages, 8 figures. v3: further minor correction

QNRs: toward language for intelligent machines

Impoverished syntax and nondifferentiable vocabularies make natural language a poor medium for neural representation learning and applications. Learned, quasilinguistic neural representations (QNRs) can upgrade words to embeddings and syntax to graphs to provide a more expressive and computationally tractable medium. Graph-structured, embedding-based quasilinguistic representations can support formal and informal reasoning, human and inter-agent communication, and the development of scalable quasilinguistic corpora with characteristics of both literatures and associative memory. To achieve human-like intellectual competence, machines must be fully literate, able not only to read and learn, but to write things worth retaining as contributions to collective knowledge. In support of this goal, QNR-based systems could translate and process natural language corpora to support the aggregation, refinement, integration, extension, and application of knowledge at scale. Incremental development of QNRbased models can build on current methods in neural machine learning, and as systems mature, could potentially complement or replace today’s opaque, error-prone “foundation models” with systems that are more capable, interpretable, and epistemically reliable. Potential applications and implications are broad