We recently developed a causal inference framework and test-the Transmission Mean Test (TMT)-to identify causal genotype-phenotype relationships in population-sampled parent-child trios, where one child per family is observed. Here, we establish the generalized TMT (gTMT) for population-sampled nuclear families, allowing multiple offspring per family. This extension focuses on detecting genetic loci with non-zero average causal effects (ACE) on child phenotypes, taking into account that siblings share similar random family-specific effects. We construct a potential outcomes trait model that considers both individual-level and family-level heterogeneity, captures additive and non-additive genetic effects, and accommodates both quantitative (continuous or count) and dichotomous traits. We design an unbiased estimate dgTMT of the ACE and develop a sampling variance estimate σ^gTMT2 to form a statistic testing the null hypothesis of no causal effect. We provide both theory and empirical evidence demonstrating that gTMT is robust to confounding factors such as the population structure and family-specific effects. We analyze nuclear families in the UK Biobank as an illustrative example of the gTMT in action. When parental genotypes are missing, we propose to further extend gTMT by using Bayesian calculations on child genotypes to model parental genotypes as intermediate random variables.

The process by which genes are transmitted from parent to child provides a source of randomization preceding all other factors that may causally influence any particular child phenotype. Because of this, it is natural to consider genetic transmission as a source of experimental randomization. In this work, we show how parent-child trio data can be leveraged to identify causal genetic loci by modeling the randomization during genetic transmission. We develop a new test, the transmission mean test (TMT), together with its unbiased estimator of the average causal effect, and derive its causal properties within the potential outcomes framework. We also prove that the transmission disequilibrium test (TDT) is a test of causality as a complementary case of the TMT for the affected-only design. The TMT and the TDT differ in the types of traits that they can handle and the study designs for which they are appropriate. The TMT handles arbitrarily distributed traits and is appropriate when trios are randomly sampled; the TDT handles dichotomous traits and is appropriate when sampling is based on a child's trait status. We compare the transmission-based methods with established approaches for genotype-phenotype analyses to clarify conditions appropriate for each method, what conclusions can be drawn by each one, and how these methods can be used together.

The synthesis and characterisation of a group of molecules based on the skeletal structures of 4-[(4-nitrophenoxy)carbonyl]phenyl 4-methoxybenzoate and (4-nitrophenyl)-2-methoxy-4-(4-methoxybenzoyl)oxybenzoate is reported. Fluorine substituents are added to these structures and their liquid crystalline behaviour is characterised. All eight compounds reported exhibit the ferroelectric nematic phase, NF, and in four of them the antiferroelectric phase labelled NX is observed. These include rare examples of enantiotropic NF and NX phases, and several examples of the direct NF-isotropic transition. The addition of a fluorine substituent reduces the nematic-isotropic transition temperature, and this is attributed to the reduction in both shape anisotropy and the ability of the molecules to form antiparallel dimers. The effect of the fluorine substituents on the NF and NX phases is less regular and interpreted in terms of the changes to the molecular shape and electron distribution. The stability of the NX phase follows that of the NF phase in the series without a lateral methoxy group. The addition of a lateral methoxy group reduces the stability of the NF phase and completely suppresses the NX phase.

The synthesis and characterization of 12 ferroelectric nematogens based on the RM734 structural template are reported in the form of two series named nECMe and nECMeF. Within both series, the position of the methyl groups present was varied and all 12 of these compounds exhibited the ferroelectric nematic phase. In general, when modifications were made that decreased the shape anisotropy of the molecule, the value of T NI decreased in line with the literature. The behavior of T NFN/I was, however, much more complex, appearing to be directed by the substituents present, and the transition temperatures did not follow a distinct trend as modifications were made. This is particularly apparent when comparing 2ECMe and 3ECMe which both have a terminal methyl group and a lateral methoxy group: the T NFN of 3ECMe is 25 °C higher than that of 2ECMe, while their equivalent methoxy-substituted materials have transition temperatures essentially identical to one another. The properties of these materials can be justified, in general, by the model of Madhusudana and are sensitive to the electronic distribution within the compounds.

We show that development of polar order may spontaneously destroy the lamellar structure of a liquid crystal. This results in an unusual sequence of phases, with the ferroelectric nematic phase appearing below a non-polar smectic phase. The effect is related to unfavourable dipole interactions within the smectic layers and can be explained by Landau theory, in which the temperature-dependent term is non-monotonic as it is renormalised by spontaneous electric polarisation.

Synthesis and characterisation of mesogenic behaviour are reported for two homologous series of molecules based on DIO ([3-fluoro-4-(3,4,5-trifluorophenyl)phenyl] 2,6-difluoro-4-(5-propyl-1,3-dioxan-2-yl)benzoate). In both series, the terminal alkyl chain is extended from n = 0-7. The central aromatic ring is either singly or doubly fluorinated at positions ortho to the terminal 3,4,5-trifluorophenyl to give the series D(n)IO-F13 and D(n)IO-F23. All homologues except D(n)IO-F13 and D(0,1,2)IO-F23 show conventional paraelectric nematic phases, and homologues of F13 with n = 1-4 and F23 with n = 1-5 exhibit the ferroelectric nematic phase, NF, including rare enantiotropic examples (n = 1-2 and n = 1-3, respectively). The antiferroelectric NX phase is also observed in homologues n = 2-5 and n = 3-5, respectively, and is enantiotropic in all cases for the latter. Longest homologues show conventional SmA phases below the N phase. The additional F atom in the F23 materials acts to reduce TNI and TSmA-N but enhances TNF- and TNX- with respect to their F13 counterparts and this is interpreted in terms of changes to molecular shape anisotropy and enhanced intermolecular interactions. Extension of n leads to rapid destabilisation of the NF and NX phases, though the effect is not as pronounced in the F23 series such that NF persists for longer n.

In hypothesis testing, statistical significance is typically based on calculations involving p-values and Type I error rates. A p-value calculated from a single statistical hypothesis test can be used to determine whether there is statistically significant evidence against the null hypothesis. The upper threshold applied to the p-value in making this determination (often 5% in the scientific literature) determines the Type I error rate; i.e., the probability of making a Type I error when the null hypothesis is true. Multiple hypothesis testing is concerned with testing several statistical hypotheses simultaneously. Defining statistical significance is a more complex problem in this setting. A longstanding definition of statistical significance for multiple hypothesis tests involves the probability of making one or more Type I errors among the family of hypothesis tests, called the family-wise error rate. However, there exist other well established formulations of statistical significance for multiple hypothesis tests. The Bayesian framework for classification naturally allows one to calculate the probability that each null hypothesis is true given the observed data (Efron et al. 2001, Storey 2003), and several frequentist definitions of multiple hypothesis testing significance are also well established (Shaffer 1995). Soric (1989) proposed a framework for quantifying the statistical significance of multiple hypothesis tests based on the proportion of Type I errors among all hypothesis tests called statistically significant. He called statistically significant hypothesis tests discoveries and proposed that one be concerned about the rate of false discoveries1 when testing multiple hypotheses. This false discovery rate is robust to the false positive paradox and is particularly useful in exploratory analyses, where one is more concerned with having mostly true findings among a set of statistically significant discoveries rather than guarding against one or more false positives. Benjamini & Hochberg (1995) provided the first implementation of false discovery rates with known operating characteristics. The idea of quantifying the rate of false discoveries is directly related to several pre-existing ideas, such as Bayesian misclassification rates and the positive predictive value (Storey 2003).

The synthesis and characterisation of two series of cyanoterphenyl-based liquid crystal dimers containing sulfur links between the spacer and mesogenic units, the 34-{ω-[(4'-cyano-[1,1'-biphenyl]-4-yl)thio]alkyl}-[11,21:24,31-terphenyl]-14-carbonitriles (CBSnCT), and the 34-({ω-[(4'-cyano-[1,1'-biphenyl]-4-yl)thio]alkyl}oxy)-[11,21:24,31-terphenyl]-14-carbonitriles (CBSnOCT) are described. The odd members of both series show twist-bend nematic and nematic phases, whereas the even members exhibit only the nematic phase. This is consistent with the widely held view that molecular curvature is a prerequisite for the observation of the twist-bend nematic phase. The nematic-isotropic and twist-bend nematic-nematic transition temperatures are higher for the dimers containing cyanoterphenyl groups than for the corresponding cyanobiphenyl-based dimers. This change is more pronounced for the nematic-isotropic transition temperatures and is attributed to the enhanced interaction strength parameter associated with the cyanoterphenyl fragment whereas the molecular shapes, as governed by the spacer, are rather similar. The behaviour of CBS2CT appears somewhat anomalous and exhibits a higher value of the twist-bend nematic-nematic transition temperature than expected, and this is attributed to the presence of highly bent molecular conformations.

Two-dimensional (2D) supramolecular organization of asymmetric liquid crystal dimers containing two chemically different mesogenic groups, namely, cyanobiphenyl and pyreneiminomethyl phenoxy groups, linked with an oligomethylene linker of different length (six or eight -CH2- units), was studied using scanning tunneling microscopy. For this purpose, monolayers of these dimers were deposited on an HOPG substrate from their solutions in hexane by drop-casting and imaged at nanometer resolution after drying. A detailed discussion of two possible different supramolecular organizations is presented. In the case of the first one, termed the "lamellar structure", the molecules in each layer are arranged in parallel molecular rows. Comparative analysis of the monolayer structure with already reported XRD data on 3D organization of the same molecules in a single crystal revealed significant differences resulting from (i) different ordering preferences in 2D and 3D systems and (ii) effects of the interactions of the deposited molecules with the graphite substrate. A small extension of the linker by two methylene groups does not change the type of ordering in the monolayer but causes an extension of the unit cell in one direction, indicating that the lamellar structure is stabilized by rows of densely packed large aromatic pyrene units. Studies of the derivative with a longer linker (containing eight -CH2- units) also showed the possibility of the occurrence of an alternative type of its monolayer organization, termed here "aggregate structure". In this case, the monolayer consists of ordered aggregates of two molecules. According to the authors' knowledge, this type of structural organization has not yet been reported for this family of compounds. It is, however, qualitatively consistent with the already described supramolecular ordering in CBO5O.Py (CCDC 2019485), a compound closely resembling the dimers studied in this research.

The admixture model is widely applied to estimate and interpret population structure among individuals. Here we consider a "standard admixture" model that assumes the admixed populations are unrelated and also a generalized model, where the admixed populations themselves are related via coancestry (or covariance) of allele frequencies. The generalized model yields a potentially more realistic and substantially more flexible model that we call "super admixture". This super admixture model provides a one-to-one mapping in terms of probability moments with the kinship model, the latter of which is a general model of genome-wide relatedness and structure based on identity-by-descent. We introduce a method to estimate the super admixture model that is based on method of moments, does not rely on likelihoods, is computationally efficient, and scales to massive sample sizes. We apply the method to several human data sets and show that the admixed populations are indeed substantially related, implying the proposed method captures a new and important component of evolutionary history and structure in the admixture model. We show that the fitted super admixture model estimates relatedness between all pairs of individuals at a resolution similar to the kinship model. The super admixture model therefore provides a tractable, forward-generating probabilistic model of complex structure and relatedness that should be useful in a variety of scenarios.

The synthesis and characterisation of the 4-[{[4-({6-[4-(4-methoxyphenyl)phenyl]hexyl}oxy)phenyl]methylidene}amino]phenyl 4-alkyloxybenzoates is reported. These are referred to using the acronym MeOB6OIBeOm in which m denotes the number of carbon atoms in the terminal alkyloxy chain and is varied from one to ten. All ten members exhibit an enantiotropic conventional nematic (N) phase. In addition, for m = 1-9, the twist-bend nematic (NTB) phase was observed on cooling the N phase. The N-isotropic (I) and NTB-N transition temperatures decrease on increasing the length of the terminal chain and this is more pronounced for the former. This supports the view that the NTB-N transition is predominantly shape driven and this depends largely on the length and parity of the flexible spacer. The transitional behaviour of the MeOB6OIBeOm series is compared with that of the corresponding dimers based instead on a cyanobiphenyl fragment, the CB6OIBeOm series. The rich smectic polymorphism exhibited by the CB6OIBeOm series is extinguished for the MeOB6OIBeOm series. The CB6OIBeOm series shows higher values of the N-I transition temperature than the corresponding members of the MeOB6OIBeOm series whereas the values of the NTB-N transition temperatures are rather similar for corresponding members of the two series. This again suggests that the NTB-N transition is largely shape driven whereas the mixed core interaction plays a more distinct role in driving N phase formation. The promotion of smectic behaviour in the CB6OIBeOm series is attributed to the strong tendency of the cyanobiphenyl fragment to adopt anti-parallel associations.

The highly bent shape of tertiary amides offers a new design element for liquid crystals with unconventional shapes. Here we report an unusual family of liquid crystal trimers, with a marked contraction of the smectic layer spacing on cooling.

The synthesis and characterisation of 10 members of the [4[(E)-[4-[4-[omega-(4-cyanophenyl)phenoxy]alkyloxy]-3-nitrophenyl]methylideneamino]phenyl] 2,4-dimethoxybenzoates is reported in which the number of methylene units in the flexible spacer is increased from three to twelve. The mesogenic units are based on cyanobiphenyl and 3-nitrobenzylideneaniline benzoate and linked by the spacer such that their dipoles are parallel giving rise to a large longitudinal dipole moment. All 10 members of the series show a nematic phase, and the nematic-isotropic transition temperatures, T-NI, and associated entropy changes show a strong dependence on the length and parity of the spacer. This behaviour is attributed to the average shapes of the molecules and their flexibility. The heptyl member was further characterised using dielectric spectroscopy revealing a high value of dielectric permittivity reflecting the large dipole moment of the molecules and possibly indicating local short-range ferroelectric order. The synthesis and characterisation of two members of the [4[(E)-[4-[4-[3-(omega-cyanophenyl)phenoxy]alkyloxy]-4-nitrophenyl]methylideneamino]phenyl] 2,4-dimethoxybenzoates are also described for which the difference in shape between odd and even members is reduced. Both dimers are exclusively nematogenic and the difference between TNI for the odd and even member is smaller reflecting the more similar molecular shapes. The potential for developing dimers that exhibit the ferroelectric nematic phase is discussed.

The synthesis and characterisation of ten members of the 4[{[4({5[4((4-cyanophenyl)phenyl]oxy)pentoxy}yl)phenyl]methylidene}amino] phenyl 4-alkyloxybenzoates is presented. These dimers are referred to using the acronym CBO5OIBeOm in which m refers to the number of carbon atoms in the terminal chain and varies from 1 to 10. The CBO5OIBeOm series exhibits nematic (N), twist-bend nematic (N-TB), and smectic A (SmA) phases depending on the length of the terminal chain. Although the N-TB phase is observed, these dimers do not exhibit the twist-bend smectic C (SmCTB) phases. By comparison, the structurally similar CB6OIBeOm series does exhibit the SmCTB phases, and this strongly suggests that the formation of the SmCTB phase is more sensitive to molecular curvature than that of the N-TB phase. [GRAPHICS] .

We report the synthesis and phase behaviour of a series of liquid crystalline trimers containing secondary amide groups. These materials form nematic, smectic and twist-bend nematic phases and their liquid crystal behaviour appears to be primarily driven by their molecular shape, with little evidence for the influence of hydrogen bonding between the amide groups. The results show that suitable molecular design can allow for amides to be included into mesogenic materials in an analogous manner to more commonly used linking groups, such as esters and imines, offering new synthetic routes to liquid crystalline materials.

The synthesis and characterisation of two series of nonsymmetric dimers belonging to the family of compounds, the 1-(4-cyanobiphenyl-4′-yl)-ω-(4-alkylanilinebenzylidene-4′-oxy)alkanes (CBnO.m) is reported; in the acronym, n refers to the number of carbon atoms in the spacer, and m in the terminal alkyl chain. The two series reported, CB4O.m and CB8O.m, both show twist-bend nematic (NTB) and smectic phases (SmCTB-SH and SmCTB-DH). Their phase behaviour is compared to that of the CB6O.m and CB10O.m series. For each series, locally intercalated molecular packing is observed for short terminal chains and interdigitated packing for long terminal chains. The intercalated anticlinic smectic CA phase is observed for the CB8O.m and CB10O.m series. All four series exhibit the SmCTB-SH and SmCTB-DH phases for the longer terminal chains and all have an interdigitated molecular arrangement. The absence of an intercalated heliconical phase is attributed to the high viscosity associated with the network intercalated structure.

The synthesis and characterisation of two series of nonsymmetric dimers belonging to the family of compounds, the 1-(4-cyanobiphenyl-4 '-yl)-omega-(4-alkylanilinebenzylidene-4 '-oxy)alkanes (CBnO.m) is reported; in the acronym, n refers to the number of carbon atoms in the spacer, and m in the terminal alkyl chain. The two series reported, CB4O.m and CB8O.m, both show twist-bend nematic (N-TB) and smectic phases (SmCTB-SH and SmCTB-DH). Their phase behaviour is compared to that of the CB6O.m and CB10O.m series. For each series, locally intercalated molecular packing is observed for short terminal chains and interdigitated packing for long terminal chains. The intercalated anticlinic smectic C-A phase is observed for the CB8O.m and CB10O.m series. All four series exhibit the SmCTB-SH and SmCTB-DH phases for the longer terminal chains and all have an interdigitated molecular arrangement. The absence of an intercalated heliconical phase is attributed to the high viscosity associated with the network intercalated structure. [GRAPHICS] .

Six members of the 1,omega-bis(4-cyanobiphenyl-4 '-yl) alkanes are reported and referred to as CBnCB in which n = 1, 15, 16, 17, 19 and 20 and indicates the number of methylene units in the spacer separating the two cyanobiphenyl units. The behaviour of CB3CB is revisited. The temperature dependence of the refractive indices, optical birefringence and dielectric permittivities measured in the nematic, N, phase for selected homologues are reported. The dimers with n >= 15 showed an enantiotropic N phase, and for the odd members the twist-bend nematic, NTB, phase was observed. CB3CB shows a direct NTB-isotropic, I, transition, whereas for CB1CB a virtual NTB-I transition is found. The temperature dependence of the bend elastic constant, K33, measured in the oblique helicoidal cholesteric state formed by mixtures of CBnCB with a chiral additive S811, shows strong non-monotonous behaviour with a deep minimum near the transition point to the NTB phase. The minimum value of K33K33 decreases as n increases. The long even members of the CBnCB series show similar values of TNI to their odd-membered counterparts, but their estimated values of TNTBN are considerably lower. This is attributed to molecular shape and its effect on K33. {GRAPHIACAL ABSTRACT}

The syntheses and characterisation of the 4-[{[4-({n-[4-(4-cyanophenyl)phenyl]-n-yl}oxy)phenyl]-methylidene}amino]phenyl-4-alkoxybenzoates (CBnOIBeOm) are reported with n=8 and 10 and m=1-10. The two series display fascinating liquid crystal polymorphism. All twenty reported homologues display an enantiotropic nematic (N) phase at high temperature. When the length of the spacer (n) is greater than that of the terminal chain (m), the twist-bend nematic (NTB) phase is observed at temperatures below the N phase. As the length of the terminal chain is increased and extends beyond the length of the spacer up to three smectic phases are observed on cooling the N phase. One of these smectic phases has been assigned as the rare twist-bend smectic C subphase, the SmCTB-α phase. In all the smectic phases, a monolayer packing arrangement is seen, and this is attributed to the anti-parallel associations of the like mesogenic units.

We report for the first-time a series of methylthio terminated materials which exhibit the ferroelectric nematic phase.