Bounding Bloat in Genetic Programming

While many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations. A naturally occurring problem is that of bloat (unnecessary growth of solutions) slowing down optimization. Theoretical analyses could so far not bound bloat and required explicit assumptions on the magnitude of bloat. In this paper we analyze bloat in mutation-based genetic programming for the two test functions ORDER and MAJORITY. We overcome previous assumptions on the magnitude of bloat and give matching or close-to-matching upper and lower bounds for the expected optimization time. In particular, we show that the (1+1) GP takes (i) $\Theta(T_{init} + n \log n)$ iterations with bloat control on ORDER as well as MAJORITY; and (ii) $O(T_{init} \log T_{init} + n (\log n)^3)$ and $\Omega(T_{init} + n \log n)$ (and $\Omega(T_{init} \log T_{init})$ for $n=1$) iterations without bloat control on MAJORITY.Comment: An extended abstract has been published at GECCO 201

Counting Homomorphisms to Trees Modulo a Prime

Many important graph theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular independent sets and colourings. In this article we study the complexity of #_pHomsToH, the problem of counting graph homomorphisms from an input graph to a graph H modulo a prime number p. Dyer and Greenhill proved a dichotomy stating that the tractability of non-modular counting graph homomorphisms depends on the structure of the target graph. Many intractable cases in non-modular counting become tractable in modular counting due to the common phenomenon of cancellation. In subsequent studies on counting modulo 2, however, the influence of the structure of H on the tractability was shown to persist, which yields similar dichotomies. Our main result states that for every tree H and every prime p the problem #_pHomsToH is either polynomial time computable or #_pP-complete. This relates to the conjecture of Faben and Jerrum stating that this dichotomy holds for every graph H when counting modulo 2. In contrast to previous results on modular counting, the tractable cases of #_pHomsToH are essentially the same for all values of the modulo when H is a tree. To prove this result, we study the structural properties of a homomorphism. As an important interim result, our study yields a dichotomy for the problem of counting weighted independent sets in a bipartite graph modulo some prime p. These results are the first suggesting that such dichotomies hold not only for the one-bit functions of the modulo 2 case but also for the modular counting functions of all primes p

On Counting (Quantum-)Graph Homomorphisms in Finite Fields of Prime Order

We study the problem of counting the number of homomorphisms from an input graph $G$ to a fixed (quantum) graph $\bar{H}$ in any finite field of prime order $\mathbb{Z}_p$. The subproblem with graph $H$ was introduced by Faben and Jerrum~[ToC'15] and its complexity is still uncharacterised despite active research, e.g. the very recent work of Focke, Goldberg, Roth, and Zivn\'y~[SODA'21]. Our contribution is threefold. First, we introduce the study of quantum graphs to the study of modular counting homomorphisms. We show that the complexity for a quantum graph $\bar{H}$ collapses to the complexity criteria found at dimension 1: graphs. Second, in order to prove cases of intractability we establish a further reduction to the study of bipartite graphs. Lastly, we establish a dichotomy for all bipartite $(K_{3,3}\backslash\{e\},\, {domino})$-free graphs by a thorough structural study incorporating both local and global arguments. This result subsumes all results on bipartite graphs known for all prime moduli and extends them significantly. Even for the subproblem with $p=2$ this establishes new results.Comment: 84 pages, revised title and mainly the Introduction and the section on partially surjective homomorphism

Destructiveness of Lexicographic Parsimony Pressure and Alleviation by a Concatenation Crossover in Genetic Programming

For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation. First, the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with redundant parts). Second, the role and realization of crossover, which is particularly central in GP due to the tree-based representation. Whereas some theoretical work on GP has studied the effects of bloat, crossover had a surprisingly little share in this work. We analyze a simple crossover operator in combination with local search, where a preference for small solutions minimizes bloat (lexicographic parsimony pressure); the resulting algorithm is denoted Concatenation Crossover GP. For this purpose three variants of the well-studied MAJORITY test function with large plateaus are considered. We show that the Concatenation Crossover GP can efficiently optimize these test functions, while local search cannot be efficient for all three variants independent of employing bloat control.Comment: to appear in PPSN 201

Fixed-Parameter Sensitivity Oracles

We combine ideas from distance sensitivity oracles (DSOs) and fixed-parameter tractability (FPT) to design sensitivity oracles for FPT graph problems. An oracle with sensitivity $f$ for an FPT problem $\Pi$ on a graph $G$ with parameter $k$ preprocesses $G$ in time $O(g(f,k) \cdot \textsf{poly}(n))$. When queried with a set $F$ of at most $f$ edges of $G$, the oracle reports the answer to the $\Pi$-with the same parameter $k$-on the graph $G-F$, i.e., $G$ deprived of $F$. The oracle should answer queries in a time that is significantly faster than merely running the best-known FPT algorithm on $G-F$ from scratch. We mainly design sensitivity oracles for the $k$-Path and the $k$-Vertex Cover problem. Following our line of research connecting fault-tolerant FPT and shortest paths problems, we also introduce parameterization to the computation of distance preservers. We study the problem, given a directed unweighted graph with a fixed source $s$ and parameters $f$ and $k$, to construct a polynomial-sized oracle that efficiently reports, for any target vertex $v$ and set $F$ of at most $f$ edges, whether the distance from $s$ to $v$ increases at most by an additive term of $k$ in $G-F$.Comment: 19 pages, 1 figure, abstract shortened to meet ArXiv requirements; accepted at ITCS'2

Analysis of the (1 + 1) EA on subclasses of linear functions under uniform and linear constraints

Linear functions have gained great attention in the run time analysis of evolutionary computation methods. The corresponding investigations have provided many effective tools for analyzing more complex problems. So far, the runtime analysis of evolutionary algorithms has mainly focused on unconstrained problems, but problems occurring in applications frequently involve constraints. Therefore, there is a strong need to extend the current analyses and used methods for analyzing unconstrained problems to a setting involving constraints. In this paper, we consider the behavior of the classical Evolutionary Algorithm on linear functions under linear constraint. We show tight bounds in the case where the constraint is given by the OneMax function and the objective function is given by either the OneMax or the BinVal function. For the general case we present upper and lower bounds.Tobias Friedrich, Timo Kötzing, J.A. Gregor Lagodzinski, Frank Neumann, Martin Schirnec

Structure-function relationship of immunosuppressive drugs: A cautionary tale

The immunosuppressants FK506 and rapamycin bind to the same immunophilin, FK506 binding protein (FKBP), and inhibit distinct signal transduction pathways in T lymphocytes. A nonnatural immunophilin ligand, 506BD, which contains only the common structural elements of FK506 and rapamycin, was synthesized and found to be a high-affinity ligand of FKBP and a potent inhibitor of FKBP rotamase activity. Whereas 506BD does not interfere with T cell activation, it does block the immunosuppressive effects of both FK506 and rapamycin. Thus, the common immunophilin binding element of these immunosuppressants, which is responsible for rotamase inhibition, is fused to different effector elements, resulting in the inhibition of different signaling pathways. Inhibition of rotamase activity is an insufficient requirement for mediating these effects.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/38364/1/1840140326_ftp.pd

The My Active and Healthy Aging (My-AHA) ICT platform to detect and prevent frailty in older adults: Randomized control trial design and protocol

[EN] Introduction Frailty increases the risk of poor health outcomes, disability, hospitalization, and death in older adults and affects 7%¿12% of the aging population. Secondary impacts of frailty on psychological health and socialization are significant negative contributors to poor outcomes for frail older adults. Method The My Active and Healthy Aging (My-AHA) consortium has developed an information and communications technology¿based platform to support active and healthy aging through early detection of prefrailty and provision of individually tailored interventions, targeting multidomain risks for frailty across physical activity, cognitive activity, diet and nutrition, sleep, and psychosocial activities. Six hundred adults aged 60 years and older will be recruited to participate in a multinational, multisite 18-month randomized controlled trial to test the efficacy of the My-AHA platform to detect prefrailty and the efficacy of individually tailored interventions to prevent development of clinical frailty in this cohort. A total of 10 centers from Italy, Germany, Austria, Spain, United Kingdom, Belgium, Sweden, Japan, South Korea, and Australia will participate in the randomized controlled trial. Results Pilot testing (Alpha Wave) of the My-AHA platform and all ancillary systems has been completed with a small group of older adults in Europe with the full randomized controlled trial scheduled to commence in 2018. Discussion The My-AHA study will expand the understanding of antecedent risk factors for clinical frailty so as to deliver targeted interventions to adults with prefrailty. Through the use of an information and communications technology platform that can connect with multiple devices within the older adult's own home, the My-AHA platform is designed to measure an individual's risk factors for frailty across multiple domains and then deliver personalized domain-specific interventions to the individual. The My-AHA platform is technology-agnostic, enabling the integration of new devices and sensor platforms as they emerge.This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 689582 and the Australian National Health and Medical Research Council (NHRMC) European Union grant scheme (1115818). M.J.S. reports personal fees from Eli Lilly (Australia) Pty Ltd and grants from Novotech Pty Ltd, outside the submitted work. All other authors report nothing to disclose.Summers, MJ.; Rainero, I.; Vercelli, AE.; Aumayr, GA.; De Rosario Martínez, H.; Mönter, M.; Kawashima, R. (2018). The My Active and Healthy Aging (My-AHA) ICT platform to detect and prevent frailty in older adults: Randomized control trial design and protocol. Alzheimer's and Dementia: Translational Research and Clinical Interventions. 4:252-262. https://doi.org/10.1016/j.trci.2018.06.004S2522624Blair, S. N. (1995). Changes in Physical Fitness and All-Cause Mortality. JAMA, 273(14), 1093. doi:10.1001/jama.1995.03520380029031Fried, L. P., Ferrucci, L., Darer, J., Williamson, J. D., & Anderson, G. (2004). Untangling the Concepts of Disability, Frailty, and Comorbidity: Implications for Improved Targeting and Care. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 59(3), M255-M263. doi:10.1093/gerona/59.3.m255Gillick, M. (2001). Guest Editorial: Pinning Down Frailty. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 56(3), M134-M135. doi:10.1093/gerona/56.3.m134Hamerman, D. (1999). Toward an Understanding of Frailty. Annals of Internal Medicine, 130(11), 945. doi:10.7326/0003-4819-130-11-199906010-00022Fried, L. P., Tangen, C. M., Walston, J., Newman, A. B., Hirsch, C., Gottdiener, J., … McBurnie, M. A. (2001). Frailty in Older Adults: Evidence for a Phenotype. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 56(3), M146-M157. doi:10.1093/gerona/56.3.m146Panza, F., Solfrizzi, V., Barulli, M. R., Santamato, A., Seripa, D., Pilotto, A., & Logroscino, G. (2015). Cognitive Frailty: A Systematic Review of Epidemiological and Neurobiological Evidence of an Age-Related Clinical Condition. Rejuvenation Research, 18(5), 389-412. doi:10.1089/rej.2014.1637Soong, J., Poots, A., Scott, S., Donald, K., Woodcock, T., Lovett, D., & Bell, D. (2015). Quantifying the prevalence of frailty in English hospitals. BMJ Open, 5(10), e008456. doi:10.1136/bmjopen-2015-008456Varadhan, R., Walston, J., Cappola, A. R., Carlson, M. C., Wand, G. S., & Fried, L. P. (2008). Higher Levels and Blunted Diurnal Variation of Cortisol in Frail Older Women. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 63(2), 190-195. doi:10.1093/gerona/63.2.190BROWN, I., RENWICK, R., & RAPHAEL, D. (1995). Frailty. International Journal of Rehabilitation Research, 18(2), 93-102. doi:10.1097/00004356-199506000-00001Buchner, D. M., & Wagner, E. H. (1992). Preventing Frail Health. Clinics in Geriatric Medicine, 8(1), 1-18. doi:10.1016/s0749-0690(18)30494-4Kojima, G., Iliffe, S., Jivraj, S., & Walters, K. (2016). Association between frailty and quality of life among community-dwelling older people: a systematic review and meta-analysis. Journal of Epidemiology and Community Health, 70(7), 716-721. doi:10.1136/jech-2015-206717Ory, M. G., Schechtman, K. B., Miller, J. P., Hadley, E. C., Fiatarone, M. A., … Province, M. A. (1993). Frailty and Injuries in Later Life: The FICSIT Trials. Journal of the American Geriatrics Society, 41(3), 283-296. doi:10.1111/j.1532-5415.1993.tb06707.xShamliyan, T., Talley, K. M. C., Ramakrishnan, R., & Kane, R. L. (2013). Association of frailty with survival: A systematic literature review. Ageing Research Reviews, 12(2), 719-736. doi:10.1016/j.arr.2012.03.001Woodhouse, K. W., & O’Mahony, M. S. (1997). Frailty and ageing. Age and Ageing, 26(4), 245-246. doi:10.1093/ageing/26.4.245CAMPBELL, A. J., & BUCHNER, D. M. (1997). Unstable disability and the fluctuations of frailty. Age and Ageing, 26(4), 315-318. doi:10.1093/ageing/26.4.315Drey, M., Pfeifer, K., Sieber, C. C., & Bauer, J. M. (2011). The Fried Frailty Criteria as Inclusion Criteria for a Randomized Controlled Trial: Personal Experience and Literature Review. Gerontology, 57(1), 11-18. doi:10.1159/000313433Albert, M. S., DeKosky, S. T., Dickson, D., Dubois, B., Feldman, H. H., Fox, N. C., … Phelps, C. H. (2011). The diagnosis of mild cognitive impairment due to Alzheimer’s disease: Recommendations from the National Institute on Aging-Alzheimer’s Association workgroups on diagnostic guidelines for Alzheimer’s disease. Alzheimer’s & Dementia, 7(3), 270-279. doi:10.1016/j.jalz.2011.03.008Petersen, R. C., Smith, G. E., Waring, S. C., Ivnik, R. J., Tangalos, E. G., & Kokmen, E. (1999). Mild Cognitive Impairment. Archives of Neurology, 56(3), 303. doi:10.1001/archneur.56.3.303Winblad, B., Palmer, K., Kivipelto, M., Jelic, V., Fratiglioni, L., Wahlund, L.-O., … Petersen, R. C. (2004). Mild cognitive impairment - beyond controversies, towards a consensus: report of the International Working Group on Mild Cognitive Impairment. Journal of Internal Medicine, 256(3), 240-246. doi:10.1111/j.1365-2796.2004.01380.xDubois, B., Hampel, H., Feldman, H. H., Scheltens, P., Aisen, P., … Andrieu, S. (2016). Preclinical Alzheimer’s disease: Definition, natural history, and diagnostic criteria. Alzheimer’s & Dementia, 12(3), 292-323. doi:10.1016/j.jalz.2016.02.002Moher, D., Hopewell, S., Schulz, K. F., Montori, V., Gotzsche, P. C., Devereaux, P. J., … Altman, D. G. (2010). CONSORT 2010 Explanation and Elaboration: updated guidelines for reporting parallel group randomised trials. BMJ, 340(mar23 1), c869-c869. doi:10.1136/bmj.c869Gray, L. C., Bernabei, R., Berg, K., Finne-Soveri, H., Fries, B. E., Hirdes, J. P., … Ariño-Blasco, S. (2008). Standardizing Assessment of Elderly People in Acute Care: The interRAI Acute Care Instrument. Journal of the American Geriatrics Society, 56(3), 536-541. doi:10.1111/j.1532-5415.2007.01590.xRadloff, L. S. (1977). The CES-D Scale. Applied Psychological Measurement, 1(3), 385-401. doi:10.1177/014662167700100306Guralnik, J. M., Simonsick, E. M., Ferrucci, L., Glynn, R. J., Berkman, L. F., Blazer, D. G., … Wallace, R. B. (1994). A Short Physical Performance Battery Assessing Lower Extremity Function: Association With Self-Reported Disability and Prediction of Mortality and Nursing Home Admission. Journal of Gerontology, 49(2), M85-M94. doi:10.1093/geronj/49.2.m85Powell, L. E., & Myers, A. M. (1995). The Activities-specific Balance Confidence (ABC) Scale. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 50A(1), M28-M34. doi:10.1093/gerona/50a.1.m28Kendzierski, D., & DeCarlo, K. J. (1991). Physical Activity Enjoyment Scale: Two Validation Studies. Journal of Sport and Exercise Psychology, 13(1), 50-64. doi:10.1123/jsep.13.1.50Folstein, M. F., Folstein, S. E., & McHugh, P. R. (1975). «Mini-mental state». Journal of Psychiatric Research, 12(3), 189-198. doi:10.1016/0022-3956(75)90026-6Brandt, J. (1991). The hopkins verbal learning test: Development of a new memory test with six equivalent forms. Clinical Neuropsychologist, 5(2), 125-142. doi:10.1080/13854049108403297Lubben, J. E. (1988). Assessing social networks among elderly populations. Family & Community Health, 11(3), 42-52. doi:10.1097/00003727-198811000-00008Russell, D., Peplau, L. A., & Cutrona, C. E. (1980). The revised UCLA Loneliness Scale: Concurrent and discriminant validity evidence. Journal of Personality and Social Psychology, 39(3), 472-480. doi:10.1037/0022-3514.39.3.472De Vries, O. J., Peeters, G. M. E. E., Lips, P., & Deeg, D. J. H. (2013). Does frailty predict increased risk of falls and fractures? A prospective population-based study. Osteoporosis International, 24(9), 2397-2403. doi:10.1007/s00198-013-2303-zTheou, O., Stathokostas, L., Roland, K. P., Jakobi, J. M., Patterson, C., Vandervoort, A. A., & Jones, G. R. (2011). The Effectiveness of Exercise Interventions for the Management of Frailty: A Systematic Review. Journal of Aging Research, 2011, 1-19. doi:10.4061/2011/569194Cadore, E. (2014). Strength and Endurance Training Prescription in Healthy and Frail Elderly. Aging and Disease, 5(3), 183. doi:10.14336/ad.2014.0500183Cadore, E. L., Rodríguez-Mañas, L., Sinclair, A., & Izquierdo, M. (2013). Effects of Different Exercise Interventions on Risk of Falls, Gait Ability, and Balance in Physically Frail Older Adults: A Systematic Review. Rejuvenation Research, 16(2), 105-114. doi:10.1089/rej.2012.1397Gardner, M. M. (2001). Practical implementation of an exercise-based falls prevention programme. Age and Ageing, 30(1), 77-83. doi:10.1093/ageing/30.1.77Eng, J. J. (2010). Fitness and Mobility Exercise Program for Stroke. Topics in Geriatric Rehabilitation, 26(4), 310-323. doi:10.1097/tgr.0b013e3181fee736Wadlinger, H. A., & Isaacowitz, D. M. (2008). Looking happy: The experimental manipulation of a positive visual attention bias. Emotion, 8(1), 121-126. doi:10.1037/1528-3542.8.1.121MacLeod, C. (2012). Cognitive bias modification procedures in the management of mental disorders. Current Opinion in Psychiatry, 25(2), 114-120. doi:10.1097/yco.0b013e32834fda4aMensink, R. P., & Katan, M. B. (1989). Effect of a Diet Enriched with Monounsaturated or Polyunsaturated Fatty Acids on Levels of Low-Density and High-Density Lipoprotein Cholesterol in Healthy Women and Men. New England Journal of Medicine, 321(7), 436-441. doi:10.1056/nejm19890817321070